SANA, Yemen — Yemen’s president, Ali Abdullah Saleh, maintained a tenuous hold on power on Tuesday, blaming the United States and Israel for protests across the Arab world, while a prominent radical cleric joined the growing crowds demanding his ouster and called for an Islamic state.

Antigovernment protesters on Tuesday demanded the resignation of President Ali Abdullah Saleh of Yemen in the capital, Sana.

American officials expressed concern about the statement of the cleric, Abdul Majid al-Zindani, a onetime mentor of Osama bin Laden, which introduced a new Islamist element to the turmoil in a country where Al Qaeda is viewed as a grave threat. The protests that toppled leaders in Tunisia and Egypt and that now have spread to Libya, Bahrain and Oman have been largely secular in nature.

Mr. Zindani spoke on an open-air stage before several thousand antigovernment protesters, guarded by 10 men carrying AK-47s and shielded from the scorching sun by two umbrellas wielded by aides. “An Islamic state is coming,” he said, drawing cries of “God is great” from some in the crowd.

He said Mr. Saleh “came to power by force, and stayed in power by force, and the only way to get rid of him is through the force of the people.”

How much support Mr. Zindani had in the protest movement was not clear.

As the opposition held what it called “a day of rage,” the pro-government camp mustered one of its biggest crowds in weeks of turmoil. Men danced in the streets, waving aloft traditional curved daggers and replacing their opponents’ slogan — “the people want the regime to fall” — with the words “the people want Ali Abdullah Saleh.”

Obama administration officials increasingly fear the power vacuum that they believe would follow if Mr. Saleh, whose son, nephews and close allies in the Sanhan tribe control the military and intelligence agencies, departed. Mr. Zindani has long supported Mr. Saleh, and his defection, which followed that of tribal leaders and a refusal on Monday by opposition parties to join a unity government, was a sign of how quickly the president’s patronage system is dissolving, a senior administration official said.

Thomas C. Krajeski, the American ambassador to Yemen from 2004 to 2007, who just returned from a visit there, said he would put Mr. Saleh’s chances of staying in power at no better than 50-50, despite the Yemeni president’s long history as a wily survivor and tribal deal-maker during three decades in power. Mr. Krajeski, now senior vice president of the National Defense University, said that the State Department each year had studied possible successors to Mr. Saleh and “came up empty.”

A collapse of the government in Yemen would pose a serious threat to Saudi Arabia, Yemen’s far wealthier neighbor to the north, Mr. Krajeski said. “If I’m sitting in Riyadh and looking south, I would be very, very worried,” he said.

A senior Pentagon official, Garry Reid, said that given Mr. Saleh’s close cooperation on operations against Al Qaeda in the Arabian Peninsula, he saw no alternative to Mr. Saleh.

“In my view, it’s the best partner we’ll have, and hopefully it will survive,” said Mr. Reid, the deputy assistant secretary of defense for special operations and combating terrorism, in a talk at the Bipartisan Policy Center in Washington.

Mr. Saleh, for his part, sought to put distance between himself and Washington with comments that were all the more startling given the United States’ political support and military aid to his government.

“From Tunis to the sultanate of Oman,” Mr. Saleh said, the wave of protest is “managed by Tel Aviv and under the supervision of Washington.”

American officials dismissed the accusation. “We don’t think scapegoating will be the kind of response that the people of Yemen or the people in other countries will find adequate,” said Jay Carney, the White House press secretary. Mr. Carney said the Obama administration had “made clear to the leadership in Yemen, as we have to the leadership in other countries, that they need to focus on the political reforms that they need to implement to respond to the legitimate aspirations of their people.”

Privately, administration officials said they believed that Mr. Saleh was posturing to try to hang onto his job. “We’re not taking those comments that seriously,” one administration official said, speaking on the condition of anonymity.

“American diplomacy, when it’s working well, is mature enough to see when leaders are playing to their own domestic interests,” said Juan Carlos Zarate, a former Bush administration national security official now at the Center for Strategic and International Studies. “To the extent that Saleh feels he needs to distance himself from us publicly, I think we can live with that.”

For the Obama administration, the immediate preoccupation was whether Mr. Saleh could survive.

“A lot of people are really worried about what happens the day after Saleh is gone,” said Gregory D. Johnsen, a Yemen specialist at Princeton University, in a telephone interview from Cairo. Yemen is a famously well-armed country, he noted, and if a power struggle were to break out, it is hard to predict how the factions would shape up.

Yemen is very different from Egypt, where President Hosni Mubarak stepped down but the military command structure stayed very much in place, Mr. Johnsen said. If Mr. Saleh goes, his relatives and tribal allies are unlikely to hold on to their positions, he said.

The early demonstrations in Yemen were inspired by Egypt’s largely secular, pro-democracy protests. But the appearance of Mr. Zindani on Tuesday suggested a possible shift to a more overtly religious direction, Mr. Johnsen said. “Religion has a larger place in public discourse in Yemen than in most other countries in the region,” he said.

Since 2004, Mr. Zindani has been named a “specially designated global terrorist” by the United States Treasury Department, which accused him of a role in financing terrorism — a designation Mr. Saleh’s government fought to reverse. Mr. Zindani’s word as a spiritual leader carries considerable political and moral weight in Yemen.

Al Qaeda in the Arabian Peninsula, the terrorist network’s affiliate in Yemen, “is nowhere near strong enough to make a play for control of the state,” Mr. Johnsen said. But he said that if Mr. Saleh’s departure raised hopes for rapid change, the country’s rampant unemployment and poverty, growing population, shrinking oil revenue and dwindling water supply would remain.

“In a year, that could open the way for Al Qaeda to say, ‘You tried Saleh, you tried democracy, now you have to try the way of the prophet and the rule of Shariah law,’ ” Mr. Johnsen said.