Republican presidential contender Donald Trump will not be dissuaded from saying what he thinks simply because extremists use his words to recruit Muslims to their cause.

He brushed off the appearance of an African militant group's video to recruit Americans that shows him calling for Muslims to be banned from coming to the U.S. On Sunday TV news shows, Trump said it is no surprise America's enemies would exploit comments from a presidential front-runner like himself.

"The world is talking about what I've said," the billionaire real estate mogul and reality TV star told CBS's "Face the Nation" in an interview taped Friday. "And now, big parts of the world are saying, Trump is really right, at least identifying what's going on. And we have to solve it. But you're not going to solve the problem unless you identify it," he said.

The 51-minute video by al-Shabaab, an al-Qaida affiliate in East Africa, showed up Friday on Twitter. Democratic presidential candidate, former Secretary of State Hillary Clinton, claimed in the last Democratic presidential debate that another extremist group, DAESH, has been using video of Trump in its propaganda. Trump told "Fox & Friends" that the emergence since then of the al-Shabaab video does not change the fact she was wrong, claiming: "It wasn't ISIS [DAESH] and it wasn't made at the time, and she lied."

Trump told CBS that Democrats do not want to talk about extremism and claimed he will not shy away from it for the sake of depriving extremists of fodder for recruitment. "What am I going to do?" he asked. "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 the problem. And we have to solve that problem."

The al-Shabaab video, broadly seeking the support of black and Muslim-Americans, contains a clip of Trump proposing the "total and complete shutdown of Muslims entering the United States," an idea rebuffed by his rivals in both parties. Al-Shabaab is fighting the internationally backed Somali government and has carried out many guerrilla attacks there and in neighboring countries contributing troops to the effort to stabilize security.

Ben Rhodes, a deputy national security adviser in President Barack Obama's administration, said the U.S. is at war with terrorists, not Islam. "The terrorists want us to act like we're at war with Islam," he said. "That's how they recruit people. That's how they stir up grievances." Asked about the video on CNN's "State of the Union," Republican presidential contender Carly Fiorina criticized its content and misidentified the source of the propaganda as DAESH. "I find it pretty rich that this ISIS propaganda tape talks about the cruelty of the West," she said, given that group's brutality.

Trump had called for a "total and complete shutdown of Muslims entering the U.S. until our country's representatives can figure out what is going on," following recent attacks that left 14 people dead in California and 130 in Paris. Trump's comments on Muslims have been criticized for being "grossly irresponsible," as the White House branded him an unfit leader and prominent figures such as boxing legend Muhammad Ali, Facebook CEO Mark Zuckerberg and basketball legend Kareem Abdul-Jabbar lashed out at Trump's Islamophobic remarks.