House Speaker Paul Ryan said at a press conference that Trump's comments are "not who we are as a party" and violate the Constitution.
"This is not conservatism," the Wisconsin representative said, adding, "Some of our best and biggest allies in this struggle and fight against radical Islam terror are Muslims."
Senate Majority Leader Mitch McConnell said such a ban would be "completely inconsistent with American values."
"(And) to show how completely and totally unworkable it would be, King Abdullah of Jordan, a great friend and ally of ours, would presumably not be able to come to the United States," McConnell said. "How about President Ghani of Afghanistan, a great friend and ally of ours who would not be able to come to the United States. This suggestion is completely and totally inconsistent with American values."
GOP Chairman Reince Priebus said in an interview Tuesday with the Washington Examiner that he disagrees with Trump's proposal -- the first time the party's chief has publicly criticized a Trump proposal.
"We need to aggressively take on radical Islamic terrorism but not at the expense of our American values," Priebus said in the Tuesday interview.
Priebus's shot at Trump's proposal comes after months of quiet between the brash billionaire candidate and the GOP since Trump vowed not to run as a third-party candidate and signed a loyalty pledge with Priebus at his side.
But Trump has suggested in recent weeks that that pledge was conditional on the Republican Party's loyalty toward him -- which would mean not attacking Trump.
The RNC has not publicly criticized Trump since RNC spokesman Sean Spicer condemned Trump's comments disparagin former prisoner of war Sen. John McCain's service record last summer.
Ryan, for his part, suggested he would still back Trump as the Republican nominee if the candidate is nominated by his party in 2016.
Asked if he'd back Trump if he was nominated by the party in 2016, Ryan responded, "I'm going to support whoever the Republican nominee is and I'm going to stand up for what I believe in as I do that."
McConnell also said he would support whoever the GOP presidential nominee is.
Ryan's denunciation of the proposal by the party's leading presidential candidate marked a highly unusual moment in the campaign. Sitting House speakers rarely engage in presidential politics and the reprimand is particularly noteworthy coming from Ryan, the party's 2012 vice presidential nominee.
Trump released a statement Monday, calling
for "for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on." He stood by the comments at an event in Charleston, South Carolina, on Monday night, as well as in an interview with CNN on Tuesday morning.
His remarks have been widely criticized by Muslim groups, Democrats and his fellow Republican presidential contenders.
Ryan was not the first top congressional Republican leader to criticize Trump's proposal. Sen. John Cornyn of Texas, the second-ranking Senate Republican, swiftly condemned Trump's plan Monday night.
"I think it's wrong to stereotype people, I disagree. I don't think you should stereotype people," Cornyn told CNN Monday. "People are individuals. I don't think you should treat people in different categories as if they're all the same."