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JERUSALEM — Prime Minister Benjamin Netanyahu plans to meet with Donald J. Trump here on Dec. 28, but his office released a statement Wednesday night saying Mr. Netanyahu “rejects” Mr. Trump’s recent remarks about Muslims and that the meeting would go forward only as a matter of policy.

The statement came after widespread calls by opposition politicians in Israel, and even some members of Mr. Netanyahu’s governing coalition, for him to cancel the meeting in response to Mr. Trump’s call on Monday for the United States to bar all non-American Muslims from entering the country.

Mr. Trump disclosed his plans to visit Israel in a Twitter post on Tuesday.

Prior to the end of the year, I will be traveling to Israel. I am very much looking forward to it. — Donald J. Trump (@realDonaldTrump) December 9, 2015

The meeting with Mr. Netanyahu was set up two weeks ago, the prime minister’s office said. A senior Israeli official who spoke on the condition of anonymity said he did not know how long Mr. Trump would be in the country.

The Jerusalem Post reported that Mr. Trump was considering a visit to the Temple Mount, the contested Jerusalem holy site that has been a major source of friction between Israel and the Palestinians.

Battles over the site, revered by Jews as the site of their two ancient temples and by Muslims as the home of Al Aqsa Mosque and the Dome of the Rock, has helped ignite this fall’s wave of stabbings, shootings and vehicular attacks by Palestinians that have killed about 20 Jews and wounded scores more.

Mr. Netanyahu barred Israeli politicians from visiting the site, after Palestinian leaders cited such pilgrimages as evidence that Israel wanted to divide the compound, something the prime minister vehemently denies.

The Post cited “a source closely connected to organizing” Mr. Trump’s trip as saying the campaign was looking into the logistics of visiting the site. It would be unusual for an American politician to include the site on his itinerary.

Israel Radio reported that an Arab-Israeli member of Parliament, Issawi Frej, had asked Israel’s interior minister to bar Mr. Trump from entering the country. “Imagine that a state or any candidate in a country would say that entry to Jews is forbidden,” Mr. Frej said. “A racist man like that has no room among us.”

Mr. Frej was one of 37 members of Parliament — including Jews, Muslims and two lawmakers from Mr. Netanyahu’s coalition — who by late afternoon had signed a petition calling on the prime minister to cancel the meeting.

“While around the world, leaders are denouncing the racist and offensive statements made by the Republican candidate for the presidency, Netanyahu is welcoming him with open arms,” read the petition, started by Michal Rozin of the left-wing Meretz Party. The meeting, the petition alleged, “endorses Trump’s racist statements, and as such demonstrates contempt for the democratic nature of the state of Israel and for Israel’s Muslim citizens.”

Late Wednesday, the prime minister’s office released a statement saying that Israel “respects all religions and strictly guarantees the rights of all its citizens,” adding: “At the same time, Israel is fighting against militant Islam that targets Muslims, Christians and Jews alike and threatens the entire world.”

It said Mr. Netanyahu had decided this year “on a uniform policy to agree to meet with all presidential candidates from either party” who visit Israel and request a meeting. “This policy does not represent an endorsement of any candidate or his or her views,” it added. “Rather, it is an expression of the importance that Prime Minister Netanyahu attributes to the strong alliance between Israel and the United States.”

Two large opposition parties, Zionist Union and Yesh Atid, said there were no plans for their leaders to meet with Mr. Trump. Visiting candidates typically meet with the head of the parliamentary opposition as well as the prime minister and other politicians.

Several Israeli leaders had joined a panoply of American Jewish groups in denouncing Mr. Trump’s comments this week. Natan Sharansky, the former Soviet dissident who now heads the Jewish Agency and is one of Israel’s most respected figures, said Mr. Trump’s “extreme remarks” were “very dangerous.”

“We should not permit ourselves to turn our legitimate fears and threats and challenges of terror into hatred of the other, into dismissing whole national or religious groups of people,” Mr. Sharansky told The Times of Israel, a news website.

The same website quoted Michael B. Oren, a centrist member of Mr. Netanyahu’s coalition in Parliament and a former Israeli ambassador to Washington, as saying that Jews, “who have been the victims of gross and hostile generalizations throughout our history, should be the first to condemn it.”

“It’s precisely Israel,” Mr. Oren said, “that must stand up and defend not only its own peaceful Muslim population but the countless millions of Muslims who abhor terror and who are the first victims of terror.”

Even the leader of Republicans in Israel, Kory Bardash, condemned Mr. Trump’s comments as “diametrically opposed to everything America stands for,” saying, “There is room for a legitimate debate about immigration policy, but there’s no apology for what Trump said.”

Irit Pazner Garshowitz contributed reporting.