Mr Biden, who took office earlier this year, has always been critical of Brexit and regularly references his Irish heritage to express frustration at the decision to leave the bloc.
But not everyone was pleased with his explanations and responses to questions asked by reporters, including the chairwoman of the RNC, Ronna McDaniel.
Traditionally, there is no question as to whether a first-term president will run for reelection.
Thursday's press conference looked different from what Americans are used to seeing for formal presidential news conferences: the White House limited attendance due to the virus, sanitized microphones in between reporters' questions, and there were no contentious exchanges with members of the press.
"Rolling back the policies of separating children from their mothers, I make no apology for that", Biden said.
US President Joe Biden rejects criticism for rolling back Trump era border policies. By waiting until the stimulus package was passed, Biden was able to use the press conference to showcase a major achievement for his administration.
Biden returned to the topic of Trump and immigration two more times, including when pressed on his own rhetoric and policies, which have - intentionally or not - sent a more welcoming signal to migrants considering making the risky journey north.
Asked whether he expects to face Trump in another general election campaign, Biden demurred.
"I make no apologies for ending programmes that did not exist before Trump became president that have an incredibly negative impact on the law, global law, as well as on human dignity", he said. I make no apologies for ending programs that did not exist before Trump became president that have an incredibly negative impact on the law, worldwide law, as well as on human dignity.
The latest swipe from Mr Biden saw several people take to Twitter to question the UK's chances of striking a trade deal with the U.S., with one tweeting: "How's that trade deal going, Johnson?"
"We are not staying a long time", he said.
Yet on Thursday, Biden seemed eager to discuss his predecessor.
Mr. Biden said it was going to be hard to get USA troops out of Afghanistan by May 1 - a deadline set by Mr. Trump following talks with the Taliban. "We can change the lives of so many people".
On China, Mr. Biden talked about how he knew Chinese President Xi Jinping from the time they were both Vice-Presidents of their respective countries.
"That's who we are", Biden continued.
Trump did his part to remain omnipresent, calling into Laura Ingraham's Fox News show Thursday night to attack Biden's immigration policies as "inhumane" and boast about his partially built border wall.
Biden may have a few reasons for being purposefully vague about a 2024 bid.
But Biden had certain limits Thursday when it came to his 2020 rival.
"Oh, come on", he said.
"I hope everyone remembers. that if I wasn't president, you wouldn't be getting that attractive "shot" for 5 years, at best, and probably wouldn't be getting it at all".
'I don't even think about it.