The fighting between Al Qaeda militants and the Yemeni military appears to be intensifying after the Yemeni army destroyed five homes suspected of hiding Al Qaeda militants in the southwest of the country Tuesday.

The director of security for Shabwa province in Yemen told Fox News that 28 militants had been captured Wednesday by authorities, as a siege of the southern village entered its third day. Medical sources there also said four Yemeni soldiers have been killed.

However, officials denied earlier reports that U.S.-born radical cleric Anwar al-Awlaki was among those surrounded, but he is believed to be hiding out in a town 60 miles from the fighting.

Government forces moved into the village of Hawta with tanks and armored vehicles and thousands of people have fled the area to escape the fighting, which officials say is targeting a 120-man militant cell.

Militants holed up in the town are reportedly using civilians as human shields. 

Troops fired on vehicles of residents fleeing the village and another nearby trouble spot, the city of Lawder, killing two civilians and wounding three others, according to local government and medical officials.

Security officials said the homes that were destroyed were empty. The officials spoke on condition of anonymity because they weren't authorized to speak to the media.

The governor of Shabwa province Ali al-Hamadi said an Al Qaeda sniper wounded a soldier and a civilian on Tuesday as security forces advanced into the village of al-Bareeqa, a few miles away from Hawta.

An unofficial website run by government opponents, Alganob.net, reported that al-Awlaki was among those who been surrounded.

But the chief municipal official, Atiq Baouda, and the security officials denied that he was in the area under siege. The Yemeni army refused to comment on the operation.

Al-Awlaki played a key part in the failed terrorist Christmas Day attempt to take down a Detroit-bound passenger jet.

Yemen says it is waging an aggressive U.S.-backed campaign to uproot the terror network's local offshoot, which Washington considers a major threat.

Mohammed Albasha, a spokesman for the Yemen Embassy in Washington, said the operation was in response to a recent attempted attack on a liquefied natural gas pipeline.

He said the military had surrounded the area and was cutting off access in and out of the town.

"Most likely they'll enter the area in the next 24 hours," Albasha said.

He said the operation has nothing to do with al-Awlaki.

"His hometown is hundreds of miles away," Albasha said.

Monday's start of the operation coincided with a visit to Yemen by President Barack Obama's counterterrorism adviser, John Brennan, for talks with President Ali Abdullah Saleh and other senior officials.

The White House said Tuesday that Brennan's trip had nothing to do with increased military actions there.

White House spokesman Robert Gibbs said the Yemeni government has been actively involved in the struggle against extremist groups, and he believed Brennan, "extended the continued message of our support for their efforts to do so."

Fox News' Greg Palkot and The Associated Press contributed to this report.