"If you are telling me they're horrible people, horrible, racist people, I would certainly apologise if you'd like me to do that."
Morgan accused the president of causing "huge anxiety and anger in my country, because Britain First is basically a bunch of racists, fascists".
"Of course I didnt know that," Trump said.
"I know nothing about them (Britain First), I know nothing about them today, other than I read a little bit.
"Perhaps it was a big story in the UK, but in the United States it wasn't a big story.
"I did a retweet. When you do those retweets they can cause problems because you never know who's doing it to start off with."
In November last year, Trump caused uproar when he retweeted a number of videos originally posted by Jayda Fransen — the deputy leader of Britain First.
The videos included a group of Muslims pushing a boy off a roof, another of a Muslim destroying a statue of the Virgin Mary, and an immigrant Muslim violently beating a Dutch boy on crutches.
Britain First are a far-right political organisation, which is renowned for filming themselves on the streets where they have harrassed Muslims and marched through multicultural towns with Christian crosses.