The resignation of Mr. Hadi, who was elected to succeed Mr. Saleh, came less than an hour after Prime Minister Khaled Bahah said on his Facebook page that he and all of the cabinet members were stepping down, “so that we are not made party to what is going on and what will happen.” Their resignations came while a United Nations-brokered meeting to resolve the crisis was underway.

If the resignations were a gambit to force concessions from the Houthis, they apparently failed. After months of insisting they did not want to seize power from an elected government, the Houthis signaled late Thursday night that they would do just that.

According to local news reports and a Western diplomat, Houthi leaders were considering the possibility of forming a presidential council to govern the country that would include Houthi members, political parties and military officers. A Yemeni news agency, Al Masdar Online, said the Houthis had also issued a “no-fly list” of former ministers and officials who would not be allowed to leave the country.

According to the Constitution, the speaker of Parliament, Yahya al-Raye, would be required to form a caretaker government. It seemed unlikely that Mr. Raye was in any position to take charge, however, with Houthi fighters in control of key points in the capital, government buildings and the airport.

Mr. Hadi had come under increasing pressure from the Houthis, who demanded top government posts and undermined his control of the military and security agencies, according to analysts and diplomats. An official close to Mr. Hadi, who spoke on the condition of anonymity out of apparent concern about his safety, said in a telephone interview that the president believed that he had no choice but to leave office. “The president expresses his disappointment at the difficult circumstances and challenges surrounding what is going on from the conflict with the Houthis,” said the official, sounding nervous and hanging up immediately.

Mr. Hadi’s resignation was not accompanied by a new wave of violence in the capital, at least initially, although there were reports of violence in the province of Marib, an important oil-producing area east of Sana, with the Houthis clashing with Sunni tribesmen.