WASHINGTON — President Trump vowed on Thursday to overturn a law restricting political speech by tax-exempt churches, a potentially huge victory for the religious right and a gesture to evangelicals, a voting bloc he attracted to his campaign by promising to free up their pulpits.

Mr. Trump said his administration would “totally destroy” the Johnson Amendment, a 1954 law that prohibits churches from endorsing or opposing political candidates at the risk of losing their tax-exempt status.

“Freedom of religion is a sacred right, but it is also a right under threat all around us,” Mr. Trump told religious leaders at the National Prayer Breakfast. “That is why I will get rid of and totally destroy the Johnson Amendment and allow our representatives of faith to speak freely and without fear of retribution.”

Repealing the law would require approval by Congress, which could prove challenging given that Democrats, and even some Republicans, would resist what many view as an erosion of the separation between church and state.

Still, Mr. Trump’s promise to repeal the law fulfills a campaign pledge — one that became a centerpiece of his effort to mollify the religious right, which was slow to warm to his insurgent candidacy. Eliminating the measure has been a goal of many social conservatives, who argue that it unfairly restricts clergy members from expressing themselves by endorsing, or speaking out against, political candidates.

Many see government persecution in limits on their official religious activities at work, and complain that the Internal Revenue Service — an agency that the right views with a special ire — singles out churches dominated by Christian conservatives.

It was one of several checklist items that religious conservative leaders told Mr. Trump were important to them. And they reacted to his announcement with delight.

“Americans don’t need a federal tax agency to be the speech police of churches or any other nonprofit groups, who have a constitutionally protected freedom to decide for themselves what they want to say or not say,” said Erik Stanley, senior counsel for the Alliance Defending Freedom, a conservative Christian legal defense group that has opposed the Johnson Amendment.

Tony Perkins, the president of the Family Research Council, a conservative Christian group, called Mr. Trump’s pledge “outstanding — right on target.”

“Pastors should be held accountable to God alone for what they say behind the pulpit, not the I.R.S.,” he said.

Many clergy members, however, say they see no reason to lift the prohibition, because making political endorsements could divide their congregations. They say the law in effect shields them from pressure by advocacy groups and politically active congregants to make endorsements.

“It would usher our partisan divisions into the pews,” said Amanda Tyler, the executive director of the Baptist Joint Committee for Religious Liberty, a group that advocates a strict separation of church and state.

Few Americans had even heard of the Johnson Amendment when Mr. Trump turned it into a rallying cry during the campaign. He told a crowd at the Iowa fairgrounds last August, “It denies your pastors their right to free speech, and has had a huge negative impact on religion.”

No one lobbied Mr. Trump to make the amendment an issue, said Johnnie Moore, a Christian publicist who serves on the president’s evangelical advisory board. He said Mr. Trump himself fixed on it in his first campaign meeting with the board members last June at Trump Tower.

Mr. Trump asked them why they did not have the courage to speak out more during elections. When the pastors informed him that they could lose their tax-exempt status, Mr. Trump declared the law unfair.

In meetings since then between Mr. Trump and pastors, whether in public or private, Mr. Moore said, Mr. Trump consistently says, “Everybody in this country has freedom of speech, except for you.”

Churches and clergy members are free to speak out on political and social issues — and many do — but the Johnson Amendment was intended to inhibit them from endorsing or opposing political candidates.

Separately, the Free Speech Fairness Act was introduced in the House and the Senate on Wednesday. The bill would modify the Johnson Amendment by allowing churches and other charities to engage in political expression.

However, most Americans, and even most clergy members, say they do not want churches and houses of worship to engage in partisan politics. Nearly 80 percent of Americans said it was inappropriate for pastors to endorse a candidate in church, and 75 percent said churches should not make endorsements, according to a survey released in September by LifeWay Research, an evangelical polling group based in Nashville.

Moreover, 87 percent of pastors said they should not make political endorsements from the pulpit, according to a LifeWay survey conducted in 2012 of pastors in evangelical and mainline Protestant churches. (Clergy members who were Republicans were slightly more in favor of endorsements than those who were Democrats or independents.)

Pastors and churches that endorsed candidates have seemed to have little to fear from the I.R.S. The overburdened agency has little capacity to investigate every report of a violation — and there have been many.

But only one church is known to have ever lost its tax-exempt status for partisan politicking, and that was in 1995, those on all sides said. It is impossible to know how many churches the I.R.S. has investigated. The agency does not make public when it investigates a church for violations, and an I.R.S. spokesman declined to answer questions related to the Johnson Amendment on Thursday.

For years, pastors have openly defied the law on “Pulpit Freedom Sunday,” organized by the Alliance Defending Freedom. Many participating pastors send their sermons to the I.R.S. afterward.

Watchdog groups like Americans United for Separation of Church and State and the Freedom From Religion Foundation have occasionally reported violators to the I.R.S. and have regularly sent warning letters to pastors before elections reminding them of the law.

In a freewheeling speech at the National Prayer Breakfast, the president defended his immigration policy, brushed aside concern about his harsh phone calls with foreign leaders and ridiculed Arnold Schwarzenegger for his poor ratings in replacing him as host of “The Celebrity Apprentice.”

He did not mention any potential executive order on religious freedom, which critics said would restrict the rights of lesbians, gay men, bisexuals and transgender people; a draft has circulated, but administration officials have denied that it will be adopted.

Mr. Trump talked about the influence of faith in his life, referring to the family Bible, which was used when he took the oath of office. His mother, he said, read to him from that Bible during his childhood.

“America is a nation of believers,” he said. “The quality of our lives is not defined by our material success, but by our spiritual success.”

“I tell you that as someone who has had material success,” he added, before noting that many rich people are “very miserable, unhappy people.”

The breakfast with religious leaders featured the usual homilies and testimonials to the power of faith. But the proceedings took a show-business turn when Mark Burnett, the Hollywood producer, stepped to the podium to introduce the president.

Mr. Burnett recalled the influence Mr. Trump’s book “The Art of the Deal” had on him as a recently arrived immigrant from Britain. He later produced “The Apprentice” as a reality television vehicle for Mr. Trump.

The president opened his remarks with an extended reminiscence about the show, recalling that he fired an agent who had rejected Mr. Burnett’s pitch for the program. He also needled Mr. Schwarzenegger, the former governor of California, for failing to maintain his ratings. “We know how that turned out,” Mr. Trump said. “The ratings went down the tubes.”

“I want to just pray for Arnold, for those ratings,” he said.

Read more at Trump Vows to ‘Destroy’ Law Banning Political Endorsements by Churches.