The Houthi militia of Yemen has vowed to strike back after an Israeli attack killed senior members of the group’s government but appeared to leave its military leadership largely untouched.

The Israeli strike on Thursday hit a gathering of cabinet members, killing the militia’s prime minister, Ahmed al-Rahawi, and “several of his colleagues,” said Mohammed al-Bukhaiti, a senior Houthi political official, in an interview. He declined to provide further details, pending an official announcement.

Among the other cabinet members killed was the foreign affairs minister, Jamal Amer, according to a person briefed by Houthi officials and an associate of the minister briefed by a relative. Hashem Sharaf al-Din, the information minister, was also killed, according to the person briefed by Houthi officials and an associate of Mr. Sharaf al-Din briefed by a relative.

All three people spoke on the condition of anonymity because the Houthis — an Iranian-backed militia that rules much of northern Yemen with an iron fist — had not made a formal announcement confirming the deaths.

“The symbolic impact is considerable,” said Ahmed Nagi, a senior Yemen analyst at the International Crisis Group, a research institution. “The Houthis are now anxious that future strikes could extend beyond government officials to include military leaders who actually hold decision-making power within the group.”