After jihadists used his tough remarks about Muslims in a recruitment video, Donald Trump refused to back down, saying in remarks aired Sunday, "I have to say what I have to say."

The Republican presidential hopeful made the comments on CBS's "Face the Nation" after a US monitoring group said that his call for a ban on Muslims entering the US had been used in a video by Somalia's extremist Shebab group.

Trump's call for a total, if temporary, ban had drawn criticism around the globe, including from Hillary Clinton, the frontrunning Democratic candidate, who said his remarks were used by radicals in recruitment videos -- a suggestion Trump aides had sharply denied.

In the new video, the Al Qaeda-affiliated Shebab uses an excerpt from Trump's December 7 speech -- made after an attack by a radicalized couple in California killed 14 people -- to encourage Western Muslims to wage jihad, the SITE Intelligence Group reported.

READ: Donald Trump featured in new militant recruitment video

After describing Trump's call for a ban, the video goes on to say, "The West will eventually turn against its Muslim citizens."

Asked about it on CBS, the Republican frontrunner seemed to shrug his shoulders.

"What am I going to do?" Trump 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."

He said his stance had drawn wide support, and he pointed to the recent terrorist attacks in Paris and said, specifically citing the case of Brussels, that many nations were "shutting down cities that had never had a problem before."

"Maybe it's not politically correct," Trump said, but "there's a big problem out there."

Trump's inflammatory remarks last month sparked global outrage.

READ: Trump's effect on Muslim migrant debate reverberates in heartland

During a Democratic debate last month, Clinton accused Trump of being "ISIS's best recruiter," referring to the self-described Islamic State group, and said radical jihadists were "showing videos of Donald Trump insulting Islam and Muslims in order to recruit more radical jihadists."

Trump accused her of lying, but Clinton's spokeswoman insisted that his remarks were "being used in social media by ISIS as propaganda."

US media outlets were unable to find any footage to back up Clinton's initial claim.

The Shebab, who were driven out of Mogadishu in 2011, are fighting to overthrow Somalia's internationally backed government, which is protected by 22,000 African Union troops.