WASHINGTON—President Trump has signaled his support for a measure that would prohibit the U.S. government from turning to a secretive surveillance court to get wiretaps on Americans, according to a White House official, setting up a potential clash between the president and the intelligence community.

Sen. Rand Paul, the Kentucky Republican drafting the measure, told reporters Thursday that he is crafting an amendment to a coming intelligence bill that would overhaul the Foreign Intelligence Surveillance Court.

...