The context of that quote seem to be travel restrictions. In the same briefing, Trump claimed shortly before:
He called me xenophobic. He called me a racist, because he has since apologized and he said I did the right thing
CNN summarizes the claim:
Trump claimed that presumptive Democratic presidential nominee Joe Biden has apologized for having accused him of xenophobia on January 31, when Trump's administration announced its coronavirus travel restrictions on China.
CNNs factcheck concludes:
Biden has not apologized for having called Trump xenophobic. [...]
Biden's campaign announced in early April that he supports Trump's travel restrictions on China, so part of Trump's Monday claim is correct. But the Biden campaign did not say the former vice president had previously been wrong about the ban, much less apologize.
Rather, the campaign says Biden's January 31 accusations -- that Trump has a record of "hysterical xenophobia" and "fear mongering" -- were not about the travel restrictions at all.
The announcment was:
"Joe Biden supports travel bans that are guided by medical experts, advocated by public health officials, and backed by a full strategy," Kate Bedingfeld, Biden's deputy campaign manager, told CNN. "Science supported this ban, therefore he did too."
I was unable to find any evidence for any sort of letter in this regard.
Instead, it seems to be about the statement by a Biden campaign manager, which supports one of Trumps policies but did not apologize for calling Trump xenophobic.