WASHINGTON — Long one of President Trump’s most ardent defenders, the evangelist Franklin Graham voiced strenuous dissent this week about the practice of separating families at the border, even calling it “disgraceful.” His comments, along with other criticism from the evangelical community, raised the possibility that the president’s support from conservative Christians might erode as outrage mounted over the Trump administration’s “zero-tolerance” immigration policy.

But if evangelical leaders were pained by the sight of children being taken from their parents, they did not directly fault Mr. Trump.

Instead, many blamed Congress and past administrations, Republican and Democrat, and emphasized that Mr. Trump called family separation “horrible” in a tweet and that he wanted a legislative fix for immigration. And though it is too early to know the electoral consequences of the policy, few conservative Christian political leaders have been concerned that Mr. Trump will lose support among their ranks, which represent one of his most important voting blocs.

“This is not the administration’s fault,” Mr. Graham said in an interview on Monday, while reiterating his stance against family separation. “I don’t point the finger at Trump.’’

But even Mr. Trump, after weeks of pushing his administration’s policy and asserting, wrongly, that current law required family separation, retreated on Wednesday afternoon. He signed an executive order to end his administration’s policy of separating families and instead said they could be detained together indefinitely. The order said that officials would continue to criminally prosecute all who cross the border illegally, and it may face a legal challenge.

Mr. Graham had also accused lawmakers of visiting detention centers for political gain, after recent high-profile trips by Democrats. “This administration is extremely concerned,” Mr. Graham said before votes in Congress on two immigration proposals expected this week. “They’ve got to have some Democrats cross the aisle.”

Robert Jeffress, the pastor of First Baptist Dallas, who gave a controversial prayer at the opening of the United States Embassy in Jerusalem last month, said he fully supported the president’s policy. He called the separation of families “gut-wrenching” and the optics of the situation “horrible.” But he said it was more gut-wrenching to see immigrants enter the country illegally and harm or kill Americans, echoing one of the president’s prime arguments for “zero tolerance.”

Their stances underscored the delicate path evangelical leaders had to tread as they expressed deep unease about border separations, while still maintaining staunch opposition to illegal immigration and showing loyalty to a president who has consistently delivered on their policy goals.

There were some schisms beneath the unified front, however, as frustration mountedamong Hispanic evangelicals, one of the fastest-growing religious groups in the United States. Wilfredo De Jesús, who leads the largest Assemblies of God church in the country, New Life Covenant in Chicago, said that the close ties between the conservative evangelical leadership and Mr. Trump are part of the problem.

“The white evangelicals need to stand up to him and say, ‘Hey we voted for you, but you need to do something about this,’ ” Mr. De Jesús said in an interview on Monday. “I feel disappointed in them.”

Randall Balmer, professor of religion at Dartmouth College, echoed that sentiment. “The persistence of evangelical support for Trump, both his personal behavior and now his immigrations policies, finally lays to rest the illusion that the religious right was ever concerned about ‘family values,’” he wrote in a text.

The highest-level religious criticism of the border separations to date came Wednesday morning from Pope Francis, who called the Trump administration’s policy “immoral” in an interview with Reuters. ”Populism is not the solution,” he said.

In another sign of dissent, more than 600 members of the United Methodist Church signed a statement this week accusing Attorney General Jeff Sessions — whose department was charged with enforcing the separation policy — with child abuse, immorality and racial discrimination. They recommended that Mr. Sessions reclaim his values and “repair the damage he is currently causing to immigrants, particularly children and families.’’

The Faith and Freedom Coalition, the conservative religious group led by Ralph Reed, sent a letter to House lawmakers on Tuesday urging them to vote in favor of both immigration bills. Mr. Reed, the group’s chairman, said that ending the family-separation component was a part of larger immigration priorities, including the Deferred Action for Childhood Arrivals program and border security.

In language that reframed the logic of family separation for evangelical voters, who have long supported anti-trafficking measures, he said that human traffickers often posed as parents to bring children across the border illegally.

“The Democrats are so busy playing politics with the separation issue that they are ignoring the bigger problem, which is the exploitation of minor children by traffickers,” Mr. Reed said in an interview between meetings on Capitol Hill on Monday.

As the political fight plays out in Washington, it has revealed competing priorities in conservative evangelical America, the pull between political and pastoral. Immigration is not one of the core issues for Concerned Women of America, a conservative Christian political organization that campaigns against abortion and in support of Israel and religious liberty. But Penny Nance, the group’s president, called the family-separation problem “heartbreaking” and issued a statement on Tuesday calling on Congress to act.

“The whole base is suddenly involved,” she said in an interview. “People who don’t normally pay attention, you have our attention.”

The debate is also a further sign of demographic tensions in evangelical communities as the movement changes. White evangelicals have long been among the president’s most loyal supporters, while nonwhite evangelicals have often expressed frustration with his stance on matters of race and immigration.

In May, eight evangelical women from Chicago piled into a passenger van and took turns driving through the night to visit hundreds of immigrant women detained at the T. Don Hutto Residential Center in Taylor, Tex. They brought the women tamales and Puerto Rican rice, gave them Bibles and prayed.

Many of the detained women had left their children with relatives, while others had children who were already in the United States. They were struggling with guilt and confusion, said Brenda Bravatty, the pastor of an evangelical church in Chicago, Casa de Misericordia, who was on the trip.

“We encouraged them that they were going to see their children again,” she said, adding that some women had been there for more than a year. “What happens at the border, everything is destroyed for them. We have to rebuild their self confidence and trust.”

Last week, Mr. De Jesús, the Chicago pastor who has also visited the center in Texas, prayed at the National Hispanic Prayer Breakfast in Washington, where Vice President Mike Pence; Speaker Paul D. Ryan; the House Democratic leader, Nancy Pelosi; and the Senate Democratic leader, Chuck Schumer, all spoke on immigration.

Mr. De Jesús said he viewed it all as political posturing, especially before the midterms, and expressed frustration that Democrats did not overhaul immigration laws when they controlled Congress under President Barack Obama, as the Republicans do now under Mr. Trump. Hispanic evangelical pastors, he said, are fed up.

“I’m dissatisfied at how the Republicans and Democrats are using family, an institution God created, as pawns for their benefit,” Mr. De Jesús said. “This is going to continue to deteriorate, get worse before it gets better.”

Read more at Evangelical Leaders Lament Border Separations, but Stand Behind Trump.