WASHINGTON—Republican lawmakers on Tuesday expressed national-security concerns over the proposed $400 million plane that the Qatari ruling family wants to give to the U.S. for use as Air Force One, offering rare GOP resistance to a venture backed by President Trump.

The emirate, once called “a funder of terrorism” by President Trump, has spent lavishly on overhauling its global reputation.

Critics say the president is now openly enriching himself in ways that make the ethical complaints of his first term look quaint in comparison.