Donald J. Trump called on Monday for the United States to bar all Muslims from entering the country until the nation’s leaders can “figure out what is going on,” an extraordinary escalation of his harsh rhetoric aimed at members of the Islamic faith in the aftermath of the terrorist attacks in Paris and San Bernardino, Calif.

“Without looking at the various polling data, it is obvious to anybody the hatred is beyond comprehension. Where this hatred comes from and why we will have to determine,” said Mr. Trump, the leading Republican candidate for his party’s 2016 presidential nomination.

“Until we are able to determine and understand this problem and the dangerous threat it poses, our country cannot be the victims of horrendous attacks by people that believe only in jihad, and have no sense of reason or respect for human life,” he said in a statement.

A spokeswoman for Mr. Trump confirmed the authenticity of the statement. Asked what prompted it, Mr. Trump said, “death,” according to the spokeswoman.

Mr. Trump made his remarks a day after President Obama delivered a national address from the Oval Office urging Americans not to turn against Muslims in the wake of the terrorist attacks. Mr. Trump is expected to say more at a rally at the USS Yorktown in South Carolina on Monday evening to mark the anniversary of the Japanese attack on Pearl Harbor in 1941.

Experts on immigration law and policy expressed shock at the proposal Monday afternoon.

“This is just so antithetical to the history of the United States,” said Nancy Morawetz, a professor of clinical law at New York University School of Law, who specializes in immigration. “It’s unbelievable to have a religious test for admission into the country.”

She added: “I cannot recall any historical precedent for denying immigration based on religion.”

Ms. Morawetz said that the United States has long regretted policies that banned the immigration of Chinese at the end of 19th century.

“It’s a very sad chapter in American immigration history that we would think is behind us today.”

Mr. Trump has a track record of making surprising and even extreme comments whenever he is overtaken in opinion polls by other Republican candidates – as happened on Monday just hours before he issued his statement about Muslims. A new Monmouth University survey of likely Iowa Republican caucus-goers found that Mr. Trump had slipped from his recent top spot in the state, which holds the first presidential nomination contest on Feb. 1. According to the poll, Senator Ted Cruz of Texas earned 24 percent of support in the poll, while Mr. Trump had 19 percent and Senator Marco Rubio of Florida had 17 percent. But another Iowa poll released on Monday, by CNN/OCR, showed Mr. Trump with a comfortable lead but Mr. Cruz gaining ground on him.

Mr. Trump, who boasts about his strong poll numbers at the beginning of virtually every campaign speech, launched an unusually stinging attack against Ben Carson, another Republican candidate, when Mr. Carson took a lead in Iowa polls this fall; Mr. Trump, citing Mr. Carson’s memoir about his sometimes-violent youth, called him “pathological” and compared his state of mind to a child molester’s.

While several Republican presidential candidates have called for increased intelligence gathering and more aggressive investigations of suspected terrorists, as well as a halt to Muslim refugees entering the United States from Syria, Mr. Trump’s pointed suspicions about Muslims have been in a category by themselves.

At his campaign rallies, he has drawn strong applause from thousands of voters for his calls on the government to monitor mosques, and he has refused to rule out his earlier proposal to enter names of Muslims in America into a database. He has also made a series of ominous comments about President Obama’s leadership in fighting terrorism, suggesting that there was “something going on” with Mr. Obama that Americans were not aware of.

Several Republican rivals of Mr. Trump repudiated his latest remarks — something they have done for months, to little effect, after Mr. Trump has made comments or taken positions that they consider beyond the pale.

“This is just more of the outrageous divisiveness that characterizes his every breath and another reason why he is entirely unsuited to lead the United States,” said Gov. John Kasich of Ohio. Gov. Chris Christie of New Jersey called it “a ridiculous proposition, and one that won’t even be productive.” Another Republican, Senator Lindsay Graham of South Carolina, tweeted: “Every candidate for president needs to do the right thing & condemn @Realdonaldtrump’s statement.”

The proposal drew immediate condemnation from Muslim-Americans. Eboo Patel, the president of Interfaith Youth Core, based in Chicago, said, “I’m standing in a building right now where I am looking up at the Sears Tower, which was designed by Fazlur Rahman Khan,” a structural engineer originally from Bangladesh who was behind what is now known as the Willis Tower.

“What if we had barred Russians from America because of the Cold War? Who would have invented Google?” Mr. Patel asked, referring to Google’s co-founder, Sergey Brin.