Trump promised to equally put an end to the ban on other religious institutions from political activity, if they wanted to keep tax-exempt status.
He made his comments about a measure called the Johnson Amendment during remarks at the annual National Prayer Breakfast.
“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, Trump told an audience including politicians, religious leaders and guests such as Jordan’s King Abdullah.
“I will do that, remember.”
The Johnson Amendment prohibits tax-exempt organisations such as churches, charities and educational institutions from directly or indirectly participating in any political campaign in favour or against a political candidate.
It is named after Democratic former President Lyndon Johnson and is an important statutory barrier between politics and religion.
Trump previously spoke out against the amendment during the campaign and won the support of evangelical Christian leaders including Liberty University President Jerry Falwell Jr.
A change in the law would require action in the Republican-led US Congress.
After Trump’s remarks, Paul Ryan, speaker of the house of representatives, told reporters he had “always supported’’ eliminating the Johnson Amendment.
Critics including the group, Americans United for Separation of Church and State expressed, are unhappy with the move.
“President Donald Trump and his allies in the religious right seek to turn America’s houses of worship into miniature political action committees,” said the group’s executive director, Barry Lynn.
“It would also lead some houses of worship to focus on supporting candidates in exchange for financial and other aid. That would be a disaster for both churches and politics in America.”
Scrapping the Johnson Amendment has been a goal of Christian conservatives, who contend it violates free speech and religious freedom rights.
The US constitution’s First Amendment guarantees freedom of religion and bars the government from establishing an official religion.
A Trump executive order a week ago put a 120-day halt on the US refugee programme, barred Syrian refugees indefinitely and imposed a 90-day suspension on people from seven predominantly Muslim countries: Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Trump defended his directive as crucial to ensuring religious freedom and tolerance in America, and said he wanted to prevent a “beachhead of intolerance’’ from spreading in the US.
He also called terrorism a fundamental threat to religious freedom.
“The world is in trouble, but we’re going to straighten it out. OK? That’s what I do, I fix things,” he said.