In an exclusive interview with Piers Morgan aired on Good Morning Britain on Friday morning, the President said he wasn't aware of the impact of the incident as it "wasn't a big story" in the United States.
"Here's what's fair, if you're telling me they're terrible people, awful racist people, I would certainly apologise if you would like me to do that", Trump said.
Mr Trump said: "I think I'm very popular in your country".
The president said he had made the posts because of his opposition to radical Islamic terrorism.
President Donald Trump nearly apologized for retweeting inflammatory anti-Muslim and anti-immigrant videos originally shared by a British far-right political group. The retweets caused a minor diplomatic row with Prime Minister Theresa May, who denounced Trump's actions at the time.
Morgan has tantalisingly kept us waiting to see what Trump's reply to his plea was.
In extracts of the interview, Trump said: "I'm representing the United States, it's a very unfair situation". I would love to go there, as you know before this happened I was there a lot. I think people have to go out, they have to go out and really do it, and they have to win.
The full interview is set to air on Sunday night.
As for calls to ban him from visiting the country, he added: "Well, that's their problem - I could very nicely stay home".
"I don't know who they are, I don't know [anything] about them, so I wouldn't be doing that", Trump said.
However, after a bilateral meeting with May in Davos on Thursday, Trump said reports of tension in the relationship between the two nations were "a false rumor".
Morgan later asked Trump if he identified as a feminist. "They look like a lovely couple".
President Trump asserted he has "tremendous respect for women" and touted the economic opportunities women enjoy under his administration.
He also met Trump in 2008 when he won a US celebrity version of "The Apprentice, " a business-themed reality show that Trump hosted.
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