As per Uttara Khanda, Sage Durvasa had already foretold the sufferings of Rama and Sita to king Dasharatha -
Learn, O King, what happened formerly during the conflict between the
Devas and Asuras. The Daityas, whom the Suras threatened, took refuge
with the consort of Bhrigu and she, having given them a haven, they
dwelt there in safety. Seeing them thus succoured, the Chief of the
Gods, enraged, with his sharp-edged discus severed the head of
Bhrigu’s wife. “‘Beholding the murder of his consort, Bhrigu, in his
wrath, instantly cursed Vishnu, the destroyer of enemy hosts,
saying:— “Since in thine insensate fury, you have slain my spouse,
who should never have died thus, you shalt take birth in the world of
men, O Janardana, and there you shalt live separated from your consort
for many years.” “‘Having pronounced this curse, Bhrigu was overcome
with remorse and his merits being exhausted by the malediction he had
uttered, he began to propitiate that God, paying homage to the One who
delights in penance and protects his devotees. Thereafter that God
spoke, saying, “For the good of the worlds, I will be subject to your
curse.” “‘This is how the illustrious Vishnu was cursed by Bhrigu in
days of yore and descended on earth, becoming your son, O Foremost of
Monarchs. Renowned in the Three Worlds under the name of Rama, he
has to undergo the dire consequences of Bhrigu’s curse. He will
reign in Ayodhya for a long time. Those who follow him will be happy
and prosperous and, having reigned for eleven thousand years, Rama
will go to Brahmaloka. Having performed many great sacrifices,
distributing costly gifts, he, who may not be overcome by the most
powerful beings, shall establish many dynasties and he will beget two
sons by Sita.’
Sarga 51, Uttara Kanda