The announcement on Thursday was characteristically vague. It was unclear how much power Mr. Saleh would allow to be shifted to Parliament and the prime minister. Although Parliament is an elected body, Mr. Saleh has an almost complete lock on power and sometimes ignores laws it passes.
If he were to transfer significant power, it would be one of his biggest concessions yet.
Adel al-Surabi, a spokesman for the student-led sit-in in Sana, said the protesters rejected the proposal. “Leave, Mr. Saleh. This is our demand,” he said. “It’s clear.”
The mainstream political opposition did not issue an immediate official reaction and called a meeting on Thursday night to decide how to respond. But one opposition leader, Mohammed al-Sabri, said in an interview before the gathering, “The people will not accept this initiative.”
The mainstream opposition has generally been more open to compromise with the president than the thousands of protesters in the streets, who are heady with demonstrators’ successes in Tunisia and Egypt in overthrowing long-serving autocrats.
Mr. Saleh is a strong American ally against terrorism, and the American Embassy in Sana has not wavered from its stance encouraging dialogue between the protesters and the president — a recommendation the demonstrators have so far refused.
The United States has been worried about Mr. Saleh’s hold on power.
Hafez al-Bukari, a political analyst, said he thought Mr. Saleh’s latest offer was significant, but too late.
“If these concession were proposed about one month ago they might have had a big effect,” he said. “But now the protests are growing in power.”
He also said that because Mr. Saleh expected his plan to be rejected, he might have seen it as a way to appear conciliatory — especially by Western leaders — without having to make any drastic changes. Mr. Bukari also said the president might have been trying to fracture the opposition. In recent days, the mainstream opposition has been moving closer to the protesters’ uncompromising stance.
Mr. Saleh’s proposal would set up a national committee, including legislators, who would draw up a new constitution that would pass more powers to Parliament. That would include allowing legislators to name cabinet members, according to a government statement issued after the speech.
Once the constitution was drawn up, it would go to a referendum, and the changes could begin this year, the statement said.
Mr. Saleh has been rolling out concessions for weeks — including that he would step down in 2013 — but his government has also cracked down on protesters, killing about 30, according to Amnesty International.
Pressure has been steadily growing on him to step down, with 16 members of Parliament resigning from the governing party, an influential tribal sheik abandoning him and the number of protesters growing.
In his speech on Thursday, Mr. Saleh called for protesters to remain peaceful, and said that they were “the youth of the future” and “the youth of the nation.”
The audience of supporters from across the country, gathered in a stadium here, chanted, “The people want Ali Abdullah Saleh” and “We will sacrifice our blood and souls for Ali.”