However Muslim Khan, a Pakistani Taliban spokesman, told Al Jazeera that the military was "lying" about the number of dead fighters.
"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."
On Sunday, at least eight people were said to have been killed in a suspected US drone attack in South Waziristan, a border area to the southwest of Swat where pro-Taliban groups are supported.
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.
The flood of refugees is said to be the largest movement of people in Pakistan since partition from India 60 years ago.
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.
"Some of them died on the road, but no one was willing to offer us any help - neither the army nor the Taliban.
"They are both committing atrocities and cruelty against the ordinary people."
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."
Car bomb attack
On Monday, a suicide car bombing at a checkpoint in northwest Pakistan left 10 people dead.
The attack took place near the town of Darra Adam Khel, on the outskirts of Peshawar, the capital of Pakistan's North West Frontier Province (NWFP), officials said.
There has been no claim of responsibility for the bombing.
Two paramilitary soldiers and eight civilians, including a six-year-old girl, were killed.
There were also reports that the army had jammed an FM radio station run by the Taliban in Swat.
Kamal Hyder, Al Jazeera's correspondent in Peshawar, said: "It was through those FM stations that they were able to pass their information and go on a campaign of their own, a propaganda campaign."
The US has expressed support for the offensive, after calling on Pakistan to do more to root out Taliban fighters in the country who are said to plot attacks on American and Nato forces fighting in neighbouring Afghanistan.