"If you're telling me they're terrible racist people, I would certainly apologies if you'd like me to do that", he told Good Morning Britain's Piers Morgan during the interview, conducted in Davos on Thursday.
"I know nothing about them, I don't want to be involved with people (like that)", he argued adding "if you are telling me they're horrible people, horrible, racist people, I would certainly apologize if you'd like me to do that".
When questioned on his trip to the United Kingdom and the various opposition that the President would have to face, Trump said: "I hadn't heard about banning, I think a lot of the people in your country like what I stand for, [including] tough borders".
"I am often the least racist person that anybody is going to meet".
Sanders also stated that Trump didn't verify facts in the videos before sharing them.
But the third video Trump retweeted that purported to show a Muslim teenager beating up a blonde boy on crutches that was posted by Britain First's Vice-Chairman Jayda Fransen was actually of a Dutch boy beating up another Dutch boy.
The video clips Fransen tweeted however were dismissed as hoaxes.
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The interview was newsworthy, Morgan told anyone who would listen, since, according to him, it contained something rare: an apology from Trump.
"And I support you militarily very much".
Trump responded, "They are, but this was - I didn't do it".
"We're on the same wavelength, I think, in every respect", Trump said.
"I don't care" about potential protesters, Trump told Morgan in the morning show interview.
Morgan described Britain First, which presents itself as a political party but is widely seen as an extremist group targeting Muslims, as "racist".
Through all of this, Trump has never backed down from criticism of his Twitter activity. "I know nothing about them", Trump said.