Fazlullah is reported to have been wounded during an offensive in northwest Swat vally.
Major-General Athar Abbas told a news conference in the capital Islamabad that there was credible information that Fazlullah was hit, but gave no other details.
Fazlullah is considered the architect of a nearly two-year Taliban campaign to enforce a stricter interpretation of Islamic law or sharia, in the Swat Valley, and has been on the run since the military launched its offensive in the region in late April.
The first drone strike on Wednesday took place before dawn: six missiles fired at a mountaintop training camp in the Karwan Manza area of South Waziristan, killing 10 people, Pakistani intelligence officials said on condition of anonymity.
Hours later and 20km to the east, missiles hit four vehicles, killing at least 35 people Pakistan officials said were Taliban fighters, including a key commander.
It is not known whether Mehsud, wanted by the US and Pakistan, was among the dead and injured, and independent verification of the targets and casualties is difficult because the region is largely inaccessible to journalists.
More than 45 drone attacks, usually blamed on the US, have been carried out in the region since last August.
|Pakistani forces are on an offensive against the Taliban [EPA]|
South Waziristan has become the focus of the Pakistani military’s offensive against Taliban sympathisers after it launched an assault in the Swat Valley and Buner in April.
The military has been carrying out bombing runs of its own and firing mortar rounds at Taliban targets in the region as part of efforts to kill or capture Mehsud, who is blamed for organising many of the suicide attacks in Pakistan over the past few years.
Pakistani officials, however, denied signing off on Wednesday’s attacks, saying the drone raids were hurting their military campaign against Mehsud because they were alienating local tribes.
Babar Awan, Pakistan’s parliamentary affairs minister, told Al Jazeera that his country has “always objected all the drone attacks” and that was its firm stand.
“Whatever the technology used including the drones, we will not permit anybody else to do this [on Pakistani soil],” he said.