Donald Trump's Republican rivals have so far denounced his proposal to create a system for tracking Muslims in the U.S., describing the idea as "abhorrent," "revolting," and "dangerous."

“I find it abhorrent that Donald Trump is suggesting that we register people, that haunts back to a time that no one wants to go back to,” Jeb Bush said on CNBC on Friday.

“If we're just going to pick out a particular group of people based on their religion, based on their race, based on some other thing, that's setting a pretty dangerous precedent,” said Ben Carson, who is rivaling Trump atop most Republican primary polls. Carson added that wants a database tracking everyone in the country, regardless of religion.

John Kasich, who Trump attacked in a Twitter tirade late Thursday, said the Republican frontrunner is "trying to divide people" and could cost Republicans his home battleground state of Ohio.

George Pataki tweeted that the idea is "as revolting as it is un-American."

The outrage stems from Trump telling NBC News on Thursday he "would certainly implement" a Muslim registry, indicating that it would be mandatory for all Muslims in the U.S. to register.

"There should be a lot of systems, beyond databases," he added.

Trump took to Twitter Friday afternoon to say he “didn't suggest a database-a reporter did.”

I didn't suggest a database-a reporter did. We must defeat Islamic terrorism & have surveillance, including a watch list, to protect America — Donald J. Trump (@realDonaldTrump) November 20, 2015

Trump did not mention the concept of Muslim databases during a rally in South Carolina Friday afternoon.

Even Texas Sen. Ted Cruz, who at times during the 2016 race has sought to align himself with Trump, distanced himself from the proposal.

“I’m a big fan of Donald Trump's but I’m not a fan of government registries of American citizens,” he told reporters while campaigning in Iowa.

Democrats used even stronger language to denounce Trump. “This is shocking rhetoric. It should be denounced by all seeking to lead this country,” Hillary Clinton tweeted.

This is shocking rhetoric. It should be denounced by all seeking to lead this country. -H https://t.co/qs2TJI5spu — Hillary Clinton (@HillaryClinton) November 20, 2015

"This is an outrageous and bigoted statement. Mr. Trump should be ashamed of himself,” Bernie Sanders said in a statement.

"When you hear people like Donald Trump talking about wanting to do ID cards based on religion, what the hell is that?” Martin O’Malley said on MSNBC’s Morning Joe. “I mean, how is that at all American?”