"What am I gonna do?" he said in an interview with CBS News' John Dickerson. "I have to say what I have to say."
Trump also said he is not the only public figure featured in terrorist recruitment videos.
"They've used other people too," Trump told Dickerson.
The video posted online Friday by Al-Shabaab, Al-Qaeda's Somalia affiliate, includes a clip of Trump calling for a ban on Muslims entering the United States. Al Shabaab was responsible for the 2013 attack on Kenya's Westgate mall, which killed more than 65 people and wounded many more. Several of its leaders have been the target of U.S. drone strikes in recent years.
Trump's campaign had previously declined to comment on the video.
The more-than 51-minute propaganda video comes on the heels of a war of words between Trump and Democratic frontrunner Hillary Clinton over her suggestion that the real estate mogul's controversial remarks about Muslims would be used to recruit jihadis.
The video includes a clip of Trump calling for a "shutdown" of Muslims entering the United States.
At a rally Saturday evening in the Mississippi Coast Coliseum in Biloxi, Trump made no mention of the video.