For two weeks, the question of whether to yield to pleas from Saudi Arabia and order the U.S. military to strike targets in Yemen controlled by the Iran-backed Houthis has bedeviled President Trump.

A decision to go forward could open another front in the war against Iran that Mr. Trump started but has been unable to end as it spreads economic shock around the globe.

The president had wavered for weeks over the Saudi appeals for help in fighting the Houthis, who took advantage of the instability in the Middle East and reignited their war with the kingdom this summer.

But things came to a head on Thursday: Crown Prince Mohammed bin Salman, the kingdom’s de facto leader and a major ally in the Iran war, called the president to implore him, again, to step in to help blunt the rapidly advancing group, administration officials said.

Mr. Trump had met with advisers just the day before and told them he did not favor strikes. But after speaking with the Saudi crown prince, he reversed himself and told the Pentagon to prepare for airstrikes against the Houthis.

But by midday Sunday, the president appeared to have reversed himself again. There would be no U.S. airstrikes against the Houthis — at least not for the time being, according to administration officials.