Yemeni government troops trying to recapture areas held by Islamic militants have killed 12 suspected Al Qaeda members in the troubled southern province of Abyan, the Defense Ministry said Thursday.

Hundreds of militants seized the provincial capital, Zinjibar, on May 27, taking advantage of a breakdown of authority resulting from the government's battle with armed tribesmen seeking to topple the autocratic leader of more than three decades.

Yemen's crisis has deepened further since President Ali Abdullah Saleh, who has clung to power throughout months of protests against his rule, was wounded in a rocket attack on his compound nearly a week ago and flown to neighboring Saudi Arabia for urgent medical treatment.

Saleh had surgery to remove shards of wood that lodged in his chest when one of the rockets splintered a pulpit in a mosque where the president and top aides were praying.

On Thursday, Saudi and Yemeni officials in Riyadh, the Saudi capital, said Saleh's condition had stabilized enough to move him out of intensive care at the military hospital where he is being treated. The officials said Saleh, who also suffered burns, would have cosmetic surgery in the coming days. They spoke on condition of anonymity because they were not authorized to speak to the press.

The United States fears the 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.

In Abu Dhabi, U.S. Secretary of State Hillary Rodham Clinton called on all sides to honor a cease-fire. She said Washington was pushing for an "immediate, orderly and peaceful transition" in Yemen.

The militants were killed in gunbattles as government troops pressed toward the town of Zinjibar. The Defense Ministry said the 12 were killed in the Doves and Kod areas but gave no more details.

Three soldiers were wounded, provincial military officials said, speaking on condition of anonymity because they weren't authorized to release the information.

On Tuesday, the Defense ministry said its troops killed at least 30 militants just outside Zinjibar.

The Yemeni government consistently claims that the militants in Abyan are connected to Al Qaeda. But their true identity remains unclear because Yemen has numerous armed Islamic militants and not all are affiliated with the terror network.

The Obama administration has intensified the covert U.S. war in Yemen, hitting militant suspects with armed drones and fighter jets, The New York Times reported late Wednesday.

The report said Yemeni troops that had been battling militants linked to Al Qaeda in the south of the impoverished country have been pulled back to the capital, Sanaa, to support Saleh's regime.

American officials hope the strikes will help prevent militants from consolidating power.

A drone strike by U.S. special operations forces on May 5 targeted U.S.-born Al Qaeda cleric Anwar al-Awlaki, but a malfunction caused rockets to miss him by a matter of minutes, two U.S. officials told The Associated Press. The officials spoke on condition of anonymity to discuss intelligence matters.

The recent operations come after a nearly yearlong pause in American airstrikes, which were halted amid concerns that poor intelligence had led to bungled missions and civilian deaths that were undercutting the goals of the secret campaign.

Saleh authorized secret American missions in Yemen in 2009 but placed limits on their scope and has said publicly that all military operations have been conducted by his own troops.

The military officials said drones believed to belong to the United States have over the past week intensified their sorties over Abyan and the nearby province of Shabwa. Both are suspected to host militants from Al Qaeda.

The stepped-up campaign is taking place as Yemen's political crisis seriously imperils the country's stability, potentially giving Al Qaeda and other militants greater freedom of movement in the south while the government shifts its focus to defending its hold on the capital to the north.

For more than two weeks, Sanaa has been locked down, as government forces battle fighters loyal Sheik Sadeq al-Ahmar, head of the powerful Hashid tribal confederation who has emerged as a chief opponent of the president during the crisis.

Republican Guard troops and security forces sealed off the entrances of the city, barring hundreds of residents and visitors from entering.

The government initially blamed the tribesmen for the June 3 attack on President Saleh's compound, but has also blamed Al Qaeda.

The attack, which hit a mosque in the compound, killed 11 bodyguards and seriously wounded five senior officials who were worshipping alongside Saleh.

The Defense Ministry revealed Thursday that two members of Saleh's extended family were also injured in the strike. They are Kannan Saleh, a son of Yemen's central security chief, and Tarek Saleh, the son of a Republican Guard commander.