ISLAMABAD – The commander of the Taliban in Pakistan's northwestern Swat valley is alive and has not been wounded, contrary to reports by the military, his spokesman said on Thursday.

The military said early this month that it believed it had wounded the commander, named Fazlullah, who has been on the run since the military launched an offensive in the region in late April.

He's alive. He was not wounded. All of the Taliban leadership is OK, the spokesman, Muslim Khan, told Reuters by telephone from an undisclosed location.

Violence across northwest Pakistan and the spread of Taliban influence have heightened concerns about insecurity in the nuclear-armed country, a key ally in the West's mission to stabilize Afghanistan and destroy al Qaeda.

Security forces are nearing the end of an operation launched close to three months ago in the Swat valley and the nearby districts of Buner and Lower Dir, but they still face pockets of resistance in some areas.

Authorities have started helping many of the close to 2 million people displaced by the fighting return home.

The military says it has killed nearly 1,800 militants since the Swat offensive began. Independent estimates are unavailable and critics say few guerrilla leaders have been eliminated, making it more possible for them to regroup.

Khan vowed that the Swat Taliban would continue to fight there, rather than moving to the South Waziristan tribal region.

The army is preparing for a campaign against Pakistani Taliban leader Baitullah Mehsud in that region, which borders Afghanistan.

We'll fight everywhere. We have lot of fighters in South Waziristan, Khan said, referring to the overall Pakistani Taliban. They'll fight there and we'll continue our fight here.

Khan also played what he said was an audio tape of Fazlullah recorded on Wednesday. It was not possible to verify the authenticity of the recording.

Pakistani rulers and generals have carried out suppression on Pashtuns and the people of Malakand division (of North West Frontier Province) to please the United States, Fazlullah said, according to the recording.

My innocent brothers and sisters, peace cannot be restored until Islamic Shariah laws are enforced. Our goal is only to implement the Shariah laws and we're ready to sacrifice the last drops of our blood.

(Reporting by Kamran Haider; Writing by Jason Subler; Editing by Jeremy Laurence)