The United States fears that this power vacuum will give freer rein to al-Qaeda's branch in Yemen - one of the terror network's most active franchises; it has been behind two attempted terror attacks on U.S. targets.
On a visit to Egypt on Wednesday, the U.S. Joint Chiefs of Staff chairman, Adm. Mike Mullen, said Washington was particularly concerned about al-Qaeda's branch gaining a greater range of operations.
"It is incredibly dangerous and made that much more dangerous in the ongoing chaos," Mullen said.
Hundreds of thousands of Yemenis have protested daily since late January demanding the ouster of Saleh, who has ruled for nearly 33 years. Their campaign has been largely peaceful, but fighting erupted in San'a between Saleh loyalists and fighters from the most powerful tribal confederation, the Hashid, after troops moved to attack the home of the Hashid leader, Sheikh Sadeq al-Ahmar.
The fighting continued until Friday, when a rocket hit Saleh's presidential palace, wounding him and killing 11 of his guards. Saleh, in his late 60s, was taken to Saudi Arabia with severe burns and chunks of wood in his chest.
While the cease-fire has largely held in San'a, fighting has raged the last two days in Taiz, Yemen's second-largest city. Taiz has been the site of major protests, and last week government troops cracked down hard, breaking up a protesters' camp and killing more than 20.
In recent days, tribesmen from the Taiz region sympathetic to the protesters rose up and attacked government forces. Security officials said Wednesday that tribesmen were now in control of large parts of the city of one million, 150 miles south of San'a.
The fighting in Taiz underlined that the deadlock in the capital is unlikely to remain relatively peaceful for long, with Saleh's opponents pressing for a definitive end to his rule. Vice President Abed Rabbo Mansour Hadi is acting president, but Saleh did not formally hand over power, and his officials say he will return within days.
The United States and Saudi Arabia are pressing for the revival of an accord by which Hadi would formally take power, a unity government would be formed with the ruling and opposition parties, and elections would be held within two months.
But the opposition has its own divisions. Official opposition parties say they accept the deal. But the youth groups behind the massive anti-Saleh protests reject it, saying it would only keep vestiges of his regime in place.