“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.