Fazlullah is the son-in-law of Sufi Muhammad, a pro-Taliban religious leader in the North West Frontier Province where Swat is located.
Al Jazeera's Sohail Rahman, in Islamabad, said: "Whether he [Fazlullah] was there or not is still unclear."
Imran Khan, Al Jazeera's correspondent in Peshawar, said: "The army is telling us that they started to use heavy bombardment against a mountain stronghold that belongs to Mullah Fazlullah.
"Once that bombing was over they sent in helicopters and then parachuted in commandoes to take the area," he said.
"This area is home to nearly 4,000 Taliban fighters and it is home to Pakistan Taliban in the Swat valley's arms dump and training camps for suicide bombers and armed fighters. So it's really the hub.
"It's a crucial blow to the Pakistani Taliban."
Another military air attack on Tuesday killed at least eight people in a house in Sara Mhora, in South Waziristan, on the Afghan border, according to intelligence sources.
The assault is thought to have been carried out by a US drone.
Athar Abbas, Pakistan military spokesman, said that 751 opposition fighters had been killed so far in their military offensive in Lower Dir, Buner and Swat valley. Twenty-nine security personnel had also been killed in fighting.
Abbas said that a "search and destroy operation" was now underway.
'On the run'
On Monday, Rehman Malik, the country's interior minister, said that Pakistan's armed forces have put Taliban fighters "on the run" as the military stepped up its offensive in the Swat valley.
"The operation will continue until the last Taliban is flushed out," Malik said, adding that the offensive was "continuing successfully".
"Our strategy has succeeded. We haven't given them a chance. They are on the run. They were not expecting such an offensive."
However Muslim Khan, a Pakistani Taliban spokesman, told Al Jazeera that the military was "lying" about their successes.
"They simply want to impress the Obama administration, because that's where they get their money from," he said.
"The operation in Swat is being carried out at the behest of the American administration."
The escalation in operations comes as the United Nations warned of a worsening humanitarian crisis, with about one million people thought to have been forced from their homes since August last year.
Abdur Rahman, one displaced resident who fled to a refugee camp in the town of Mardan, told Al Jazeera: "People from all over - from Matta, Mingora and from everywhere - [are fleeing] on foot. Women and children and even old women and old men."
|It is unknown whether Mullah Fazlullah was in the hideout at the time of the offensive
Rustam Shah Mohmand, former ambassador to Afghanistan and security expert at the Institute of Policy Studies, told Al Jazeera: "It's a Pashtun genocide. How can you assess the success of an operation that has resulted in the displacement of one million people so far, that has caused the flattening of whole villages?
"The scars will not heal for many, many years to come.
"There will be a tremendous amount of hatred against the government because it's believed that the government perhaps created an environment in which a military operation had become so necessary.
"Pakistani Taliban would never have posed any danger to the state. That is grossly exaggerated. They do not even hold Buner. A small security force could have defeated them. Instead, the option of resorting to full-scale military operation was used by the government.
"It is a very, very disproportionate reaction."
Yousuf Raza Gilani, Pakistan's prime minister, has said the Taliban poses an existential threat to the country and has urged civilians to leave the Swat valley area to avoid casualties.
|The government has called on civilians to leave the Swat valley area [EPA]
He said the government was devoting millions of dollars to help the refugees.
"These people have left their areas to save the country - we appreciate their sacrifices," Gilani said.
"The nation is ready to provide them all required facilities."
The offensive in the Swat valley, located 130km northwest of Islamabad, the capital, is seen as a test of the government's resolve to get to grips with an increasingly powerful Taliban.
But some analysts have said the government must get results quickly and minimise civilian suffering or else it risks growing public opposition.
Mehdi Hasan, a Pakistani political analyst, told the Associated Press: "If the disappointment of the people and the resentment of displaced persons increases, then it will be difficult for the government to continue this military action."