WASHINGTON—U.S. lawmakers from both parties are challenging the Trump administration’s support for Gulf allies battling Iran-aligned fighters in Yemen, putting new pressure on the U.S. president to scale back ties with Saudi Arabia during an especially sensitive time.

A bipartisan group of senators plan to demand answers on Wednesday from Secretary of State Mike Pompeo after he backed Saudi Arabia and the United Arab Emirates over the objections of most of his Yemen experts.

In...