An ongoing offensive is taking place in Yemen, where U.S.-born radical cleric Anwar al-Awlaki is believed to be hiding, a Yemeni official has confirmed to Fox News.

Earlier Tuesday, a senior U.S. official had no information to confirm a report that al-Awlaki, the first American on the CIA kill or capture list,  was cornered.

The Yemeni Army moved into the village of Hawta with tanks and armored vehicles and thousands have fled the area to escape the fighting, which is part of the government's U.S.-backed campaign to uproot a 120-man militant cell.

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

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

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

An unofficial website run by government opponents, Alganob.net, had reported that al-Awlaki, who is believed to be connected to the Fort Hood shooter and the Christmas Day bomber, had been surrounded.

But U.S. officials denied that he was in the area under siege. The Yemeni Army refused to comment on the operation.

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.

Fox News' Catherine Herridge and The Associated Press contributed to this report.