Donald Trump is considering the possibility of setting up a commission to "take a very serious look" at radical Islamic terrorism and his proposals to temporarily bar Muslims from entering the United States, even floating the name of former New York City mayor Rudy Giuliani to spearhead the operation.

"We have to be extremely careful," Trump told Fox News in a phone interview Wednesday when asked about his calls for a Muslim ban. "In fact, I'm thinking about setting up a commission perhaps headed by Rudy Giuliani to take a very serious look at this problem. But this is a worldwide problem. And we have to be smart."

Giuliani, who was New York City's mayor during the terrorist attacks that hit the World Trade Center on September 11, 2001, endorsed Trump last month, ahead of the New York primary.

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"I'm Rudy Giuliani. I mean a lot in New York politics. I endorse Donald Trump, but I'm not a part of the campaign," the former mayor told CNN in April.

In his Fox interview, Trump, now the presumptive Republican nominee, added that his proposed plan on stopping Muslims from coming onto U.S. soil was just a "temporary ban."

"If you don't want to discuss the problem, then we're never going to solve the problem," he said. "It's a real problem. So we'll figure it out, and we will get it going."

Trump's controversial proposals have received worldwide condemnation in recent weeks.

The newly-elected Muslim mayor of London, Sadiq Khan, condemned Trump's views as "ignorant" earlier this week.

"[M]y concern is he's playing to the hands of extremists who say it's not compatible to be Western and be a mainstream Muslim," Khan told the BBC in an interview.

Trump responded to Khan's comments in a separate interview Friday afternoon with Fox News radio host Brian Kilmeade, suggesting that the London mayor is "denying" the existence of Islamic extremism.

"I assume he denies there is Islamic terrorism," he said. "There is Islamic radical terrorism all over the world right now. It's a disaster what's going on. I assume he is denying that. I assume he is like our president that's denying it's taking place."

In the same interview, Trump also seemed to soften his language on his Muslim ban proposal, which he first mentioned last December in a press release.

"It's a temporary ban, it hasn't been called for yet, nobody's done it," Trump said. "This is just a suggestion until we find out what's going on."

Ahead of his Thursday meeting in Washington, D.C. with top GOP lawmakers, Trump also previewed his approach to House Speaker Paul Ryan, who said last week that he was "not ready" to back the presumptive nominee.

"I think I'm doing very fine with Paul Ryan. I have a lot of respect for Paul Ryan," Trump told Fox & Friends. "We're going to have a meeting tomorrow. We'll see what happens. If we make a deal, that would be great. And if we don't, we'll trudge forward like I've been doing and winning, you know, all the time."

Despite Trump's attempts to court Republican legislators to his side, some have refused to be won over -- including Nebraska Sen. Ben Sasse, who has called for a third-party candidate to jump into the general election race and run against the billionaire and the eventual Democratic nominee.

Of Sasse, Trump told Fox News, "he's a very nasty person -- I mean, he's got a nasty mouth, but, you know, not too many people know him."

Trump won Nebraska's GOP primary Tuesday night, picking up all of the state's 36 delegates.