The video purportedly by Somali terrorist group al-Shabaab uses historic civil rights era footage of Malcolm X and new footage of Trump to label the United States a racist society.
It comes just after Trump called, in the wake of ISIS-connected terror attacks in Paris and California, to ban all Muslims from entering the United States.
Trump dismissed the new video in an interview aired Sunday on CBS' "Face the Nation."
"They use other people, too," Trump said. "What am I going to do? I have to say what I have to say. And you (know) what I have to say? There's a problem. We have to find out what is a problem. And we have to solve that problem."
Two weeks ago, Hillary Clinton drew scrutiny when she said during a Democratic presidential debate that ISIS is using Trump's position on Muslims in recruiting videos.
There's no evidence that has happened yet, despite the al-Shabaab video -- a fact Trump used in a Sunday Twitter critique of Clinton.
Trump tweeted: "Hillary Clinton lied last week when she said ISIS made a D.T. video. The video that ISIS made was about her husband being a degenerate."
He then followed up: "Al-Shabbab, not ISIS, just made a video on me - they all will as front-runner & if I speak out against them, which I must. Hillary lied!"
On CBS, meanwhile, Trump told host John Dickerson that his criticism of Muslims is gaining traction and opening eyes.
"Look, there's a problem. I bring it up. Other people have called me and say, 'You have guts to bring it up because frankly, it's true but nobody wants to get involved,'" Trump said.
"Now people are getting involved. People that are on different persuasions than me right now, John, are saying, 'You know, maybe Trump isn't wrong. We want to examine it.'"
Ben Carson, a retired neurosurgeon vying for the GOP nomination, told ABC's Martha Raddatz on "This Week" that political correctness is the problem -- but also that politicians need to watch what they said.
"Political correctness will destroy us if we don't wake up," he said Sunday. "We should all be careful about what we say, but the fact of the matter is, let's not get so concerned about how offended our enemies are. And let's pay a whole lot more attention to who we are and how do we protect our people here in the United States."
Florida Sen. Marco Rubio seemed to dismiss Trump's role in the video, saying Sunday his GOP rival didn't create radical jihadists.
"Those radical jihadists do not exist because of Donald Trump or any other campaign, they were going to be around no matter what because they have a radical ideology and they're pursuing it violently around the world," he said at an event in Milford, New Hampshire. "So ultimately, he's not the cause of radical jihadists."