I am posting some direct references excluding subtle references from Valmiki Ramayana where he has described Rama as Bhagavaan Vishnu, the supreme. It is for those astikas who fall prey to various crooked fellows' trap that Valmiki hasn't considered Rama as Bhagavaan.
1.Devatas request Vishnu to be born as sons of Dasharatha (whole sarga)
त्वान्नियोक्ष्यामहे विष्णो लोकानां हितकाम्यया।
राज्ञो दशरथस्य त्वमयोध्याधिपते: प्रभो:।।
धर्मज्ञस्य वदान्यस्य महर्षिसमतेजस:।
तस्य भार्यासु तिसृषु ह्रीश्रीकीर्त्युपमासु च।।
विष्णो पुत्रत्वमागच्छ कृत्वाऽऽत्मानं चतुर्विधम्।
तत्र त्वं मानुषो भूत्वा प्रवृद्धं लोककण्टकम्।
अवध्यं दैवतैर्विष्णो समरे जहि रावणम्।।1.15.18-20।।
O Vishnu! We pray for the welfare of all the worlds. Dasaratha is a righteous king of ayodhya who has tejasa like rishis.
Please manifest yourself into into four and incarnate as four sons of his three wives who resemble hri, shree and kirti.
"O Vishnu! assuming the human form, kill Ravana in the battle. He has become like a thorn to the worlds and is invincible by devas.
एवं दत्वा वरं देवो देवानां विष्णुरात्मवान्।
मानुषे चिन्तयामास जन्मभूमिमथात्मन:।।
तत: पद्मपलाशाक्ष: कृत्वाऽऽत्मानं चतुर्विधम्।
पितरं रोचयामास तथा दशरथन्नृपम्।।1.15.29-30।।
Bhagavaan Vishnu,the supreme being,thus having given boon to devatas, thought of the place where he was to incarnate himself as a human in this loka. Then, bhagavan with eyes like lotus petals was pleased to make himself into four forms and to choose king Dasaratha as his father.
2. Devatas requesting Narayana to incarnate as Dasharatha’s son.
इत्येतद्वचनं श्रुत्वा सुराणां विष्णुरात्मवान्।
पितरं रोचयामास तदा दशरथं नृपम्।।
स चाप्यपुत्रो नृपतिस्तस्मिन्काले महाद्युति:।
अयजत्पुत्रियामिष्टिं पुत्रेप्सुररिसूदन:।।
स कृत्वा निश्चयं विष्णुरामन्त्र्य च पितामहम्।
अन्तर्धानं गतो देवै: पूज्यमानो महर्षिभि:।।1.16.8-10।।
Having heard the words of devatas, Vishnu chose king Dasaratha as his father.
Then, Dasaratha, having great brilliance, the destroyer of enemies, who had no sons was performing a particular putriyA iShti for getting sons. After Vishnu had decided (to incarnate) and he was worshipped by devatas and maharshis, he disappeared bidding farewell to Brahma.
3.Four Brothers are manifestations of Vishnu
प्रोद्यमाने जगन्नाथं सर्वलोकनमस्कृतम्।
कौसल्याऽजनयद्रामं सर्वलक्षणसंयुतम्।।
विष्णोरर्धं महाभागं पुत्रमैक्ष्वाकुवर्धनम्।
कौसल्या शुशुभे तेन पुत्रेणामिततेजसा।।
यथा वरेण देवानामदितिर्वज्रपाणिना।
भरतो नाम कैकेय्यां जज्ञे सत्यपराक्रम:।।
साक्षाद्विष्णोश्चतुर्भागस्सर्वैस्समुदितो गुणै:।
अथ लक्ष्मणशत्रुघ्नौ सुमित्राऽजनयत्सुतौ।।
वीरौ सर्वास्त्रकुशलौ विष्णोरर्धसमन्वितौ।
पुष्ये जातस्तु भरतो मीनलग्ने प्रसन्नधी:।।
सार्पे जातौ च सौमित्री कुलीरेऽभ्युदिते रवौ।
राज्ञ: पुत्रा महात्मानश्चत्वारो जज्ञिरे पृथक्।।1.18.10-15।।
Kausalya gave birth to a son: a form of Vishnu, bhagavaan of the entire universe
who received obeisance from all the worlds and was adorned with all auspicious signs, the venerable one to perpetuate the Ikshvaku kula. Kausalya glowed with the undiminished lustre of her son, just as Aditi with her son Indra, the foremost among devas&
the wielder of thunder. As an incarnation of the fourth part of Visnu, imbued with all virtues, and armed with truth Bharata was born to Kaikeyi. Sumitra gave birth to Lakshmana & Satrughna who were heroic, skilled in the use of all weapons and endowed with the facets of Visnu.
Bharata endowed with pure intellect was born in meena lagna & pushya nakshtra. Lakshmana & Shatrughna were born in karka lagna & ashlesha nakshatra.
4.Bhagavan Rama is sakshat Parabrahman as described in the Upanishads
सूर्यस्यापि भवेत्सूर्यो ह्यग्नेरग्नि प्रभोः प्रभुः।
श्रियः श्रीश्च भवेदग्र्या कीर्तिः कीर्त्याः क्षमाक्षमा।।
दैवतं दैवतानां च भूतानां भूतसत्तमः।
तस्य के ह्यगुणा देवि वने वाप्यथवा पुरे।।2.44.15-16।।
O Devi!Rama is the Sun of the Sun,fire of the fire,king of kings, prosperity of the prosperous,the fame of the famous,forbearance of the forbearing,god of the gods & supreme among all beings.
Whether he dwells in the forest or in the city, he has no demerit whatsoever.
5. Garuda ji introduces himself to Shri Rama as his Sanatana sakha.
अहं सखा ते काकुत्स्थ प्रियः प्राणो बहिश्चरः।
गरुत्मानिह सम्प्राप्तो युवाभ्यां साह्यकारणात्॥6/50/46
न च कौतूहलं कार्य्यं सखित्वं प्रति राघव।
कृतकर्म्मा रणे वीर सखित्वमनुवेत्स्यसि॥ 6/50/57
O Rama! I am your friend Garuda and have come here to help you.(46)
There is no need to be curious about this friendship. O Veera! After this war, you will come to know about our maitri.(57)
6.Ravana says Rama is saakshat Narayaana
यस्य विक्रममासाद्य राक्षसा निधनं गताः।
तं मन्ये राघवं वीरं नारायणमनामयम्॥ 6/72/11
Due to whose valour, rAkShas have been killed; I understand him (Rama) as Narayana, the Anamaya, who takes away all miseries.
7. The shlokas below clearly state that Lakshman ji is Vishnu’s amsha. This corroborates the description of Balakanda.
शक्त्या ब्राह्म्यापि सौमित्रिस्ताडितस्तु स्तनान्तरे।
विष्णोरचिन्त्यं स्वं भागमात्मानं प्रत्यनुस्मरत्॥6/59/112
अथैवं वैष्णवं भागं मानुषं देहमास्थितम्|
अथ वायुसुतः क्रुद्धो रावणं समभिद्रवत्॥ 6/59/114
After being hit by brahmashakti in his chest, Lakshmana remembered his own self, a incomprehensible unit of Bhagavaan Vishnu.
Ravana could not lift Lakshmana because Lakshmana is a manifestation of Bhagavaan Vishnu’s unit. Thus, Hanuman, fuming in anger, reached out near Ravana.
आश्वस्तश्च विशल्यश्च लक्ष्मणः शत्रुसूदनः।
विष्णोर्भागममीमांस्यमात्मानं प्रत्यनुस्मरत्॥ 6/59/122
Lakshamana, the killer of enemies, after being revived and healthy, remembered himself as an axiomatic unit of bhagavaan Vishnu.
8. Mandodari says that Rama is Narayana himself
यदैव हि जनस्थाने राक्षसैर्बहुभिर्वृतः ।
खरस्तव हतो भ्राता तदैवासौ न मानुषः ॥ 6/114/9
व्यक्तमेष महायोगी परमात्मा सनातनः ।
अनादिमध्यनिधनो महतः परमो महान् ॥
तमसः परमो धाता शङ्खचक्रगदाधरः ।
श्रीवत्सवक्षा नित्यश्रीरजय्यः शाश्वतो ध्रुवः ॥
मानुषं रूपमास्थाय विष्णुः सत्यपराक्रमः ।
सर्वैः परिवृतो देवैर्वानरत्वमुपागतैः ॥
सर्वलोकेश्वरः श्रीमान् लोकानां हितकाम्यया ।
सराक्षसपरीवारं हतवांस्त्वां महाद्युतिः ॥ 6/114/14-17
Mandodari tells her husband’s dead body-
When your brother Khara was killed by Rama in Janasthana with many a demon,it became clear that Rama is really not a human.
Rama is a great yogi,Supreme Being (परमात्मा),eternal(सनातन), having no beginning,middle or end (अनादिमध्यनिधनो),
the greatest being the one extemely luminous beyond the material world, the caretaker of everyone. Rama is Vishnu who holds a conch, a disc and a mace is subordinate having the Shrivatsa chihna on his chest, eternally associated with Devi Shri (Lakhmi/ Seeta).
He is the one who can’t be conquered, an eternal one, the constant one, who is the might of truth, the lord of entire creation, has killed you (ravana).
9. Brahmadi Devatas tell Rama that he is Shri Vishnu who had taken avataras-
कर्ता सर्वस्य लोकस्य श्रेष्ठो ज्ञानवतां वरः |
उपेक्षसे कथं सीतां पतन्तीं हव्यवाहने |
कथं देवगणश्रेष्ठमात्मानं नावबुध्यसे ||
O the creator of entire creation, o the greatest among scholars!
Why don’t you understand your true self, the greatest among devatas, and why do you neglect Seeta who is falling into the fire?
ऋतधामा वसुः पूर्वं वसूनां च प्रजापतिः |
त्वं त्रयाणां हि लोकानामादिकर्ता स्वयम्प्रभुः ||
You were the prajapati Ritadhaama among vasus and you are certainly swayamprabhu brahma, the creator of all creations.
रुद्राणामष्टमो रुद्रः साध्यानामपि पञ्चमः |
अश्विनौ चापि ते कर्णौ चन्द्रसूर्यौ च चक्षुषी ||
You are the eighth rudra among rudras and fifth among saadhyas. Two Ashvinas are your ears and, Sun and Moon are your eyes.
अन्ते चादौ च लोकानां दृश्यसे त्वं परन्तप |
उपेक्षसे च वैदेहीं मानुषः प्राकृतो यथा ||
You are seen in the beginning and end of the creations, you are ignoring vaidehi just like a material human.
#Rama's_stuti_by_brahma
(ब्रह्मकृता रामस्तुतिः)
भवान्नारायणो देवः श्रीमांश्चक्रायुधो विभुः |
एकशृङ्गो वराहस्त्वं भूतभव्यसपत्नजित् ||
You are Narayana,the omnipresent Bhagavan, holding disc (chakra). You are Varaha(slayer of hiranyaksha),the winner of enemies of past and future.
अक्षरं ब्रह्म सत्यं च मध्ये चान्ते च राघव |
लोकानां त्वं परो धर्मो विष्वक्सेनश्चतुर्भुजः ||
You are akshara brahma, satya. You are present in middle and end. You are the greatest dharma of people, you are four handed vishwaksena.
शार्ङ्गधन्वा हृषीकेशःपुरुषःपुरुषोत्तमः |
अजितःखड्गधृग्विष्णुःकृष्णश्चैव बृहद्बलः ||
You hold Sharnga bow. You are Hrishikesha(the controllet of senses).You're Purusha (supreme soul),the greatest being, http://undefeated.You 're Vishnu holding sword and Krishna with great might.
सेनानीर्ग्रामणीश्च त्वं बुद्धिःसत्त्वं क्षमा दमः |
प्रभवश्चाप्ययश्च त्वमुपेन्द्रो मधुसूदनः||
You are the commander of armies and inducer of http://people.You  are mind,power,forbearance & might. You are the beginning and end.
You are the younger brothe of Indra, i.e., http://Vamana.You 're the slayer of demon Madhu.
इन्द्रकर्मा महेन्द्रस्त्वं पद्मनाभो रणान्तकृत् |
शरण्यं शरणं च त्वामाहुर्दिव्या महर्षयः ||
You are indrakarma (doer of noble jobs like those of Indra’s),
mahendra, http://padmanabha.You  make wars to come to an end.
सहस्रशृङ्गो वेदात्मा शतजिह्वो महर्षभः |
त्वं यज्ञस्त्वं वषट्कारस्त्वमोङ्कारःपरन्तप ||
You're the soul of vedas(like a great bull with hundred tongues and thousand horns,indicating hundred & 1000s of veda recensions).
You are the Yajnya, vaShaTkAra and pranava. You are the one who hurts his enemies.
प्रभवं निधनं वा ते न विदुः को भवानिति |
दृश्यसे सर्वभूतेषु ब्राह्मणेषु च गोषु च ||
दिक्षु सर्वासु गगने पर्वतेषु वनेषु च |
सहस्रचरणः श्रीमाञ्शतशीर्षः सहस्रदृक् ||
They don’t know your beginning and end and who you are. You are seen in brahmanas, cows and all beings. You are seen in all directions, sky, mountains, forests. You are the supreme deity with thousands of feet, hundreds of heads and thousands of eyes.
त्वं धारयसि भूतानि वसुधां च सपर्वताम् |
अन्ते पृथिव्याः सलिले दृश्यसे त्वं महोरगः ||
You lift all creations, earth with its mountains. You are seen at the end of the earth, on the great serpant in water.
त्रीँल्लोकान्धारयन्राम देवगन्धर्वदानवान् |
अहं ते हृदयं राम जिह्वा देवी सरस्वती ||
O Rama! You lift all the three worlds with devas, gandharvas and rakshasas. I (Brahma) am your heart and Saraswati is your tongue.
देवा गात्रेषु लोमानि निर्मिता ब्रह्मणा प्रभो |
निमेषस्तेऽभवद्रात्रिरुन्मेषस्तेऽभवद्दिवा ||
Prabho! Devas, who are created by brahma, are hair in your limbs. When you shut your eyes, night was created and when you opened your eyes, day was manifested.
संस्कारास्तेऽभवन्वेदा न तदस्ति त्वया विना |
जगत्सर्वं शरीरं ते स्थैर्यम्ं ते वसुधातलम् ||
Your comprehensions became vedas who is not existent without you. Your body is all the creation and you stay is the plane of earth.
अग्निः कोपः प्रसादस्ते सोमः श्रीवत्सलक्षण |
त्वया लोकास्त्रयः क्रान्ताः पुराणे विक्रमैस्त्रिभिः ||
O the one with shrivatsa - chihna! Your anger is Agni, your serenity is moon. In ancient times, all the three worlds were surpassed by you in three steps (in vAmana avatara).
महेन्द्रश्च कृतो राजा बलिं बद्ध्वा महासुरम् |
सीता लक्ष्मीर्भवान्विष्णुर्देवः कृष्णः प्रजापतिः ||
Indra was made king (by you) after defeating great demon king bali. Sita is Devi Lakshmi and you are Vishnudeva, Krishna, prajaapati.
वधार्थं रावणस्येह प्रविष्टो मानुषीं तनुम् |
तदिदं नः कृतं कार्यं त्वया धर्मभृतां वर ||
You have come in this human form to kill ravana. That work of ours has been completed by you, the foremost among righteous ones.
निहतो रावणो राम प्रहृष्टो दिवमाक्रम |
अमोघं बलवीर्यं ते अमोघस्ते पराक्रमः ||
O Rama! Ravana is slayed, (therefore) being pleased, come back to vaikuntha. Your might and valour is successful (which never goes in vain).
अमोघास्ते भविष्यन्ति भक्तिमन्तश्च ये नराः|
ये त्वां देवं ध्रुवं भक्ताःपुराणं पुरुषोत्तमम्||
ये नराःकीर्तयिष्यन्ति नास्ति तेषां पराभवः|| (6/120/6-33)
Those who're your devotees, shall always be successful.They'll never vanish who sing your ancient glories with devotion in you.
Bhagavan’s Vaikuntha gaman
वैष्णवीं तां महातेजस्तद्वाकाशं सनातनम् ।
त्वं हि लोकगतिर्देव न त्वां केचित् प्रजानते ॥
ऋते मायां विशालाक्षीं तव पूर्वपरिग्रहाम् ।
त्वामचिन्त्यं महद्भूतमक्षय्यं सर्वसङ्ग्रहम्।
यामिच्छसि महातेजस्तां तनुं प्रविश स्वयम् ॥
पितामहवचः श्रुत्वा विनिश्चित्य महामतिः ।
विवेश वैष्णवं तेजः सशरीरः सहानुजः ॥
ततो विष्णुमयं देवं पूजयन्ति स्म देवताः ।
साध्या मरुद्गणाश्चैव सेन्द्राः साग्निपुरोगमाः ॥ (7/110/9-13)
Brahma said -
"O Rama! You alone are the final shelter for the whole creation! None knows You truly, except Your Maya, Your consort Sita.”
You can’t be perceived. You are the greatest being, imperishable.
You are the one who possesses everything. You enter in the form as per your wish.
Listening to the words of Pitamaha Brahma, Rama entered into the form of Vishnu with his body and younger brothers.
Thereafter, Devas, Sadhyas, Marudganas along with Indra, Agni and other foremost among devas worship vishnumaya bhagavaan.
I know that it will fall on the deaf ears of crooked ones, non-believers and pseudo seculars. It is only meant for devotees and their understanding.
Translations are for basic understading of the gist.
॥श्रीरामार्पणमस्तु॥
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