Saleh flew to Saudi Arabia for surgery shortly after its King Abdullah brokered a cease-fire late Saturday. The truce held for just hours.
In the latest violence, the office of powerful opposition tribal leader Sheik Sadeq al-Ahmar said three of his supporters were shot dead in the tense Hassaba neighborhood in the north of the capital. The district is headquarters for al-Ahmar's tribal operation.
Three other shooting deaths occurred late Sunday. A defecting military official said government gunmen opened fire on their checkpoint.
The six killings belied an offer by the acting president — Vice President Abed Rabbo Mansour Hadi — to withdraw government forces from the area. It has seen some heaviest fighting in Yemen's four months upheaval.
Government officials said Hadi was meeting again Monday with security officials in an attempt to arranged a cease-fire that would hold.
Checkpoints were spread all along the road leading to the Hassaba neighborhood, which has been virtually a closed military area since May 23 as intense fighting broke out in the district.
Residents trying to return to their homes were fired on by rooftop snipers and forced to flee yet again, said a military officer from a defecting unit that was guarding access to the tribal chief's house.
While unable to enter the district, an Associated Press reporter who reached the checkpoint could see broken electricity pylons and shops and buildings pockmarked by mortar shrapnel.
Regardless of joyous celebrations Sunday, many Yemenis feared Saleh, a masterful political survivor, would yet return — or leave the country in ruins if he cannot. Hanging in the balance was a country that even before the latest tumult was beset by deep poverty, malnutrition, tribal conflict and violence by an active al-Qaida franchise with international reach.
Saleh underwent successful surgery on his chest to remove jagged pieces of wood that splintered from a mosque pulpit when his compound was hit by rockets on Friday. He was being treated in Riyadh, the Saudi capital.
The stunning rocket attack, which the government first blamed on tribal fighters and later on al-Qaida, killed 11 bodyguards and seriously injured five senior officials worshipping at Saleh's side.
Deputy Information Minister Abdu al-Janadi said Saleh would return and assume duties after treatment, though experts on Yemeni affairs questioned whether a return is possible in the face of so much opposition.
Saleh's sudden departure raised many questions, including whether his Saudi hosts want him to return. The Saudis have backed Saleh and cooperated in confronting al-Qaida and other threats, but they are now among those pressing him to give up power as part of a negotiated deal. Saudi Arabia has watched with concern the anti-government protests that have spread to other neighboring countries like Bahrain and is eager to contain the unrest on its doorstep.
An opposition party official said Sunday that international mediators, including the United States and Saudi Arabia, tried to get Saleh to sign a presidential decree passing power to his vice president before he left for Saudi Arabia — a strong indication that they are trying to push Saleh from power permanently.
Saleh refused to sign the declaration, offering only a verbal agreement, but the negotiations delayed his departure, the official said.
The president's absence raised the specter of an even more violent power struggle between the armed tribesmen who have joined the opposition and loyalist military forces under the command of Saleh's son and other close relatives. Street battles between the sides had already pushed the political crisis to the brink of civil war.
Late Sunday, opposition figures and ruling party officials said negotiations had begun based on a U.S.-backed Gulf Arab plan to end the crisis with Saleh's resignation. Saleh rejected that plan three times after first agreeing to sign it. His departure could allow Yemen's powerful Gulf neighbors to push it forward. Details remained murky.
The two sides said Saleh was expected to remain in Saudi Arabia for two weeks, one for treatment and another for meetings, but it remained unclear if he will return to Yemen,
Yemen's unrest began as a peaceful protest movement that the government at times used brutal force to suppress, killing at least 166 people, according to Human Rights Watch. It transformed in the past two weeks into armed conflict after the president's forces attacked the home of a key tribal leader and one-time ally who threw his support behind the uprising. The fighting turned the streets of the capital into a war zone.
Other forces aligned against Saleh at the same time. There were high-level defections within his military, and Islamist fighters took over at least one town in the south in the past two weeks.
In Taiz, Yemen's second-largest city, dozens of gunmen attacked the presidential palace on Sunday, killing four soldiers in an attempt to storm the compound, according to military officials and witnesses. They said one of the attackers was also killed in the violence. The attackers belong to a group set up recently to avenge the killing of anti-regime protesters at the hands of Saleh's security forces.
Elsewhere in the south, gunman ambushed a military convoy, killing nine soldiers, officials said. They spoke on condition of anonymity because they were not authorized to talk to the media.