Ms. Hammill said she had received a call from the International Committee of the Red Cross early Monday saying that Mr. Coombs was at the Sana airport and was preparing to leave Yemen. She was able to speak to her son on Monday afternoon, after he had arrived in Oman.

“I cannot describe how happy I am,” she said.

A State Department spokeswoman, Marie Harf, confirmed that Mr. Coombs was in Muscat, the capital of Oman, telling reporters in Washington that “he is in stable condition.”

Mr. Coombs has written for publications including The Intercept, The American Prospect and Time magazine.

The Obama administration has said a number of Americans have been detained by the Houthis, a Shiite rebel group that took control of Yemen’s capital and forced the United States-backed Yemeni government from power earlier year.

American officials have not released details on the identities of the others in Houthi custody.

The video of Ms. Prime, the abducted Frenchwoman, was the first time Ms. Prime had been seen publicly since she and a Yemeni translator were seized Feb. 24 in a brazen daytime abduction in Sana. The translator, identified by news agencies as Sherine Makkaoui, was freed March 10 in the southern city of Aden.