Mr. Hadi lost control of the capital, Sana, to the Houthi forces months ago, and he finally escaped last month to take refuge among supporters in Aden. Then on Wednesday he disappeared again as the Houthi forces closed in, surfacing Thursday night in Saudi Arabia. On Friday, he landed in Sharm el Sheikh, Egypt, to represent Yemen at an Arab League meeting, but it was unclear whether he would return to Yemen anytime soon.

The Houthis were also reported to be making gains in the restive southern provinces of Abyan and Shabwa, which had been expected to pose fierce resistance. Both provinces are home to pockets of Sunni Muslim extremists, including Al Qaeda’s Yemeni branch, and the extremists loath the Houthis as heretics for following a variant of Shiite Islam.

The Houthis represent a minority among Yemen’s mostly Sunni Muslims, but the group has gained momentum by forming an alliance with Yemen’s former president, Ali Abdullah Saleh. He has helped enlist important parts of the military and security services still loyal to him to fight alongside the Houthis against Mr. Hadi’s forces.

On Thursday, the Houthi leaders sought to showcase their public support in the capital by holding a rally to condemn the Saudi Arabian air campaign. Thousands attended, suggesting that the movement may not be easy to crush through airstrikes alone.

Image President Abdu Rabbu Mansour Hadi of Yemen arrived in Saudi Arabia on Thursday. Credit... Saudi Press Agency

The Saudi-led coalition on Friday extended its airstrikes to three military bases controlled by forces loyal to Mr. Saleh and the Houthis in the central province of Marib, according to news reports and local tribal leaders. There were reports of strikes against the Houthi’s home base in the north as well.

Pentagon officials said late Friday that two Saudi airmen were rescued by the American military after they ejected from their plane over the Gulf of Aden.