"The militants are on the run," he said.
There has been no confirmation of Fazlullah's whereabouts following the attack, but his spokesman has said he still commands his forces in the region.
Fazlullah is the son-in-law of Sufi Muhammad, a local religious leader who negotiated a controversial deal with the government under which a stricter interpretation of sharia would be implemented in the Swat valley.
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 air attack on Tuesday killed at least eight people in a house in Sara Mhora in South Waziristan, near the Afghan border, according to intelligence sources.
The attack is thought to have been carried out by an unmanned US drone.
Abbas said that 751 opposition fighters had been killed so far during the military offensive in Lower Dir, Buner and Swat valley.
|It is unknown whether Mullah Fazlullah was in the area at the time of the offensive
Twenty-nine security personnel had also been killed in fighting which began less than two weeks ago.
Muslim Khan, a spokesman for the Pakistani Taliban, told Al Jazeera on Monday 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 latest fighting came as the United Nations refugee agency said that more than 500,000 people had been registered as displaced since May 2.
The newly registered internally displaced Pakistanis join another 500,000 who fled fighting in North West Frontier Province before the military began its offensive.
The UN's World Food Programme (WFP) said it was doubling its shipments of emergency food to the newly displaced, but warned that more funds would be needed to feed the stranded over the next two to three months.
"It's a Pashtun genocide," Rustam Shah Mohmand, former ambassador to Afghanistan and a security expert at the Institute of Policy Studies, told Al Jazeera.
"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 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.