WASHINGTON — President Trump on Thursday will ease restrictions on political activity by tax-exempt churches and charities, White House officials said, but has backed away from a broader religious liberty order that would have allowed faith-based organizations and companies to avoid serving or hiring gay people.

Conservative religious leaders who were fierce supporters of Mr. Trump’s candidacy had pushed the president to provide faith organizations with much more sweeping relief from Obama-era regulations that protect gay men, lesbians and others from discrimination.

Instead, in an executive order, Mr. Trump will offer a vague promise to “protect and vigorously promote religious liberty.” He will also direct federal agencies to exempt some religious organizations from Affordable Care Act requirements that provide employees with health coverage for contraception.

By making those promises to mark the National Day of Prayer at the White House, Mr. Trump is offering a partial remedy to the anger inside some religious communities toward federal laws they believe require them to put aside beliefs about homosexuality, contraception or other issues.