After reading Shri Rama's lamentations about Sita mata on the sea shore before Lakshmana I am damn sure that he just wanted to prove to the world about her being pure and pious when he refused to accept her.
He was missing her badly and was desperate to be reunited with her.
This part is love
https://www.valmikiramayan.net/utf8/yuddha/sarga5/yuddha_5_frame.htm
Those who felt bad after reading that part please go through this one
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