A growing number of influential Republicans are denouncing Donald Trump’s proposal to block Muslims from entering the U.S., including House Speaker Paul Ryan, former Vice President Dick Cheney and the head of the Republican National Committee.

"I don't agree," RNC Chair Reince Priebus told the Washington Examiner about Trump's proposal. “We need to aggressively take on radical Islamic terrorism but not at the expense of our American values."

"This is not conservatism," Ryan said at a news conference with House Republicans Tuesday. "What was proposed yesterday is not what this party stands for and, more importantly, it’s not what this country stands for.”

“His whole notion that somehow we need to say no more Muslims and just ban a whole religion goes against everything we stand for and believe in,” Cheney told radio host Hugh Hewitt.

A spokesman for former President George W. Bush pointed to a number of instances in which Bush talked about the importance of separating the Muslim faith from terrorist acts and the many contributions of Muslim Americans. The spokesman, Freddy Ford, added, “President Bush spoke a lot about this during his presidency, and he won't be weighing in anew now -- or commenting on or giving oxygen to anything of Trump’s bluster.”

Trump did a number of interviews Tuesday morning defending his proposal that calls for a "total and complete shutdown of Muslims entering the United States.” He likened it to President Franklin Roosevelt’s actions against Japanese and Germans in America during World War II, but stopped short of saying he supported internment camps.

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“We're not talking about Japanese internment camps. No, not at all,” Trump said on MSNBC’s “Morning Joe.” “But we have to get a hand around a very serious problem. And it's getting worse. And you will have more World Trade Centers and you will have more bigger than the World Trade Center if we don't toughen up, smarten up, and use our heads.”

None of the 2016 candidates has yet to express support for the measure, with many speaking out forcefully against it.

Jeb Bush said Trump is "unhinged."

Donald Trump is unhinged. His "policy" proposals are not serious. — Jeb Bush (@JebBush) December 7, 2015

Florida Senator Marco Rubio tweeted this response:

I disagree with Donald Trump's latest proposal. His habit of making offensive and outlandish statements will not bring Americans together. — Marco Rubio (@marcorubio) December 8, 2015

Chris Christie: “Again, this is the kind of thing that people say when they have no experience and don’t know what they’re talking about. We do not need to endorse that type of activity, nor should we,” he said on Michael Medved’s radio program.

Ohio Governor John Kasich, who has been the most aggressive attacker of Trump, tweeted this:

South Carolina Senator Lindsey Graham said on MSNBC's "Morning Joe," If you want to make America great again, reject this without any doubt or hesitation."

He added that Trump supporters aren't getting "a strong man who's going to fix all of our problems" but "someone who is making it harder to win a war we can't afford to lose, that's a wrecking ball for the Republican party, who's a xenophobic, race baiting, religious bigot."

Former GOP presidential nominee Mitt Romney tweeted, "On Muslims, @realDonaldTrump fired before aiming. @SpeakerRyan is on target."

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But not all Republicans disagree with Trump, signaling that the idea will garner support from some in the Republican Party, including many of Trumps supporters.

Republican presidential candidate Ted Cruz, who has been reluctant to cross Trump's path, didn't shun Trump.

“Well, that is not my policy. I've introduced legislation in the Senate that would put in place a three-year moratorium on refugees coming from countries where ISIS or al Qaeda control a substantial amount of territory,” he said Monday.

Cruz did "commend" Trump for his focus on border security, adding, " do not believe the world needs my voice added to that chorus of critics."

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Republican media personality Ann Coulter tweeted her support.

My best birthday gift! Donald Trump Calls For ‘Complete Shutdown’ of Muslim Entry to U.S. https://t.co/fGPBNcQNbm — Ann Coulter (@AnnCoulter) December 8, 2015

And radio and television host Laura Ingraham predicted this latest controversy will not hurt Trump among his supporters.

Anyone who thinks @realDonaldTrump comments will hurt him don't know the temperature of the American ppl. — Laura Ingraham (@IngrahamAngle) December 8, 2015

But Trump's remarks have caused such a stir that Republicans who usually remain neutral in the primary race have taken a rare stance.

New Hampshire Republican Party Chair Jennifer Horn tweeted:

South Carolina Republican Party Chairman Matt Moore, a neutral arbitrator in the primary, had this to say: