Up to 15,000 troops have been deployed to take on 4-5,000 militants.
Pakistani forces have been waging an air and ground campaign
The army said it had killed 55 more militants on Saturday, having said that more than 140 militants had died in earlier clashes.
A BBC correspondent says that with phone connections to the Swat valley down, it is difficult to get independent information on the fighting, and there is no way to verify the army's claims.
The fighting has already displaced some 200,000 people, while a further 300,000 are estimated to be on the move or about to flee, the UN says.
Sitara Imran, minister for social welfare in North West Frontier Province, called the exodus "one of the huge displacements, internal displacements in the world".
'Feeling helpless'
"This is not a normal war," Prime Minister Gilani told reporters on Saturday, Reuters news agency reports, "this is a guerrilla war."
"This is our own war. This is war for the survival of the country," he said.
The BBC's Mark Dummett in Islamabad says that for the first time since the military launched the offensive against the Taleban in the Swat valley, the fighting has spread into the centre of Mingora.
An indefinite curfew is preventing people from fleeing the area, but the military says it will lift the curfew for seven hours on Sunday for people to leave.
"We are feeling so helpless, we want to go but can't," Mingora resident Sallahudin Khan told Reuters news agency.
"We tried to leave yesterday after authorities relaxed the curfew for a few hours, but we couldn't as the main road leading out of Mingora was literally jammed with the flood of fleeing people."
The army has also accused the Taleban of holding the civilian population hostage and blocking their exit.
Mobile phone networks, water and electricity have all been cut in the town which is normally home to half a million people. There are fears that food and medicine will run out if the fighting does not end soon.
Our correspondent says the government is hoping for a quick victory, while it still has the support of the Pakistani people.
The US says the militants in northern Pakistan pose a direct threat to its security, and has demanded they be confronted.
Pakistani military spokesman Gen Athar Abbas said the military's objective was to eliminate the militants from the Swat valley and also the neighbouring districts of Dir and Buner.
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