The order also mandates regulatory relief to religious employers that object to contraception, such as Little Sisters of the Poor.
It does not include provisions to allow government agencies and businesses to deny services to gay people in the name of religious freedom, as was feared by some civil liberties and gay rights groups.
The American Civil Liberties Union said in a statement it would file a lawsuit challenging Trump's order.
Trump, addressing religious leaders in a signing ceremony at the White House, said: "We will not allow people of faith to be targeted, bullied or silenced any more".
"No one should be censoring sermons or targeting pastors," he said.
Trump's order directs the Internal Revenue Service to "alleviate the burden of the Johnson Amendment," the White House said in reference to a 1954 law sponsored by Lyndon Johnson, then a Texas senator who later became president.
Under the tax code, organizations that enjoy tax-free status, such as churches, are prohibited from participating in a political campaign or supporting any one candidate for elective office.
This includes a ban on making financial contributions to campaigns and candidates, but the law does allow certain non-partisan political activity such as voter registration or get-out-the-vote drives.
Trump would need Congress to rescind the Johnson Amendment, but he can instruct his administration not to enforce it through executive order.
(Reporting by Ayesha Rascoe and Daniel Trotta; Editing by Susan Heavey and James Dalgleish)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)