Over the last decade, Christians in the United States have grown increasingly alarmed about the persecution of other Christians overseas, especially in the Middle East. With each priest kidnapped in Syria, each Christian family attacked in Iraq or each Coptic church bombed in Egypt, the clamor for action rose.

During the campaign, President Trump picked up on these fears, speaking frequently of Christians who were refused entry to the United States and beheaded by terrorists of the Islamic State: “If you’re a Christian, you have no chance,” he said in Ohio in November.

Now Mr. Trump has followed through on his campaign promise to rescue Christians who are suffering. The executive order he signed on Friday gives preference to refugees who belong to a religious minority in their country, and have been persecuted for their religion. The president detailed his intentions during an interview with the Christian Broadcasting Network on Friday, saying his administration is giving priority to Christians because they had suffered “more so” than others, “so we are going to help them.”

But if Mr. Trump had hoped for Christian leaders to break out in cheers, that is, for the most part, not what he has heard so far. A broad array of clergy members has strongly denounced Mr. Trump’s order as discriminatory, misguided and inhumane. Outrage has also come from some of the evangelical, Roman Catholic and mainline Protestant leaders who represent the churches most active in trying to aid persecuted Christians, The New York Times reported.

By giving preference to Christians over Muslims, religious leaders have said the executive order pits one faith against another. By barring any refugees from entering the United States for nearly four months, it leaves people to suffer longer in camps, and prevents families from reuniting. Also, many religious leaders have said that putting an indefinite freeze on refugees from Syria, and cutting the total number of refugees admitted this year by 60,000, shuts the door to those most in need.

“We believe in assisting all, regardless of their religious beliefs,” said Bishop Joe S. Vásquez, the chairman of the committee on migration for the United States Conference of Catholic Bishops.

Jen Smyers, the director of policy and advocacy for the immigration and refugee program of Church World Service, a ministry affiliated with dozens of Christian denominations, called Friday a “shameful day” in America’s history.

It remains to be seen whether Mr. Trump’s executive order will find more support in the pews. During the campaign, Mr. Trump successfully mined many voters’ concern about national security and fear of Muslims. He earned the votes of four out of every five white evangelical Christians, and a majority of white Catholics, exit polls showed.

Christian leaders who defended Mr. Trump’s executive order were rare this weekend. One of the few was the Rev. Franklin Graham, the son of the evangelist Billy Graham and the president of Samaritan’s Purse, an evangelical aid organization. Mr. Graham has long denounced Islam as “evil,” and in July 2015 proposed a ban on Muslims entering the United States as a solution to domestic terrorism, months before Mr. Trump made his first call for the same.

In a statement on Saturday, Mr. Graham said of refugees: “We need to be sure their philosophies related to freedom and liberty are in line with ours.” He added that those who follow Sharia law — a set of beliefs at the core of Islam — hold notions “ultimately incompatible with the Constitution of this nation.”

Jim Jacobson, the president of Christian Freedom International, which advocates for persecuted Christians, applauded the executive order and said: “The Trump administration has given hope to persecuted Christians that their cases will finally be considered.”

Among the claims Mr. Trump made at his campaign rallies was that the Obama administration had denied refugee status to Christians, and had given preference to Muslims.

“How unfair is that? How bad is that?” he told supporters at a rally in St. Clairsville, Ohio, interlaced with boasts about his “tremendous evangelical support.”

The contention was consistent with the conspiracy theories held by some conservative Christians that Mr. Obama was secretly a Muslim, and that he was turning a blind eye to the suffering of Christians while using the reins of government to increase the Muslim population of the United States.

But the claim is simply untrue. In 2016, the United States admitted almost as many Christian refugees (37,521) as Muslim refugees (38,901), according to the Pew Research Center.

While only about one percent of the refugees from Syria resettled in the United States last year were Christian, the population of that country is 93 percent Muslim and only five percent Christian, according to Pew. And leaders of several refugee resettlement organizations said during interviews that it takes 18 months to three years for most refugees to go through the vetting process to get into the United States. Many Syrian Christians got into the pipeline more recently.

“We have no evidence that would support a belief that the Obama administration was discriminating against Christian populations, said the Rev. Scott Arbeiter, the president of World Relief, the humanitarian arm of National Association of Evangelicals.

His organization has resettled thousands of Muslim refugees, with the help of a network of 1,200 evangelical churches. Mr. Arbeiter said that World Relief is opposed to “any measure that would discriminate against the most vulnerable people in the world based on ethnicity, country of origin, religion, gender or gender identity. Our commitment is to serve vulnerable people without regard to those factors, or any others.”

He said that World Relief had already gathered 12,000 signatures from evangelical Christians for a petition opposing Mr. Trump’s executive order.

“We’re going to call out to our network, the 1,200 churches that are actively involved, he said, “and ask them to use their voices to change the narrative, to challenge the facts that drive the fear so high that people would accept this executive order.”