Pakistan's government signed a peace agreement with the Swat Taleban in February, allowing Sharia law there, which was sharply criticised by Washington.
The militants then moved towards the capital, Islamabad, causing further alarm.
Up to 15,000 troops have been deployed in the Swat valley and neighbouring areas to take on 4,000-5,000 militants.
The military has said it intends to "eliminate" the Taleban fighters.
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.
The government also said on Saturday that refugee camps would be set up in Peshawar, the capital of North West Frontier Province, and to the north-east in Naushara.
Footage on local television showed people at one camp desperately looting UN supplies including blankets and cooking oil.
'Road jammed'
Earlier, fighting was reported to have reached the biggest town in the region, Mingora, which the army has been trying to recapture.
The army said it had killed 55 more militants on Saturday, having said that more than 140 militants had died in earlier clashes.
Some 15,000 troops have been deployed to fight the Taleban
Due to the intensity of the fighting and the cutting of phone networks, it is difficult to get independent information on the fighting or verify the army's claims, correspondents say.
Prime Minister Yusuf Raza Gilani told reporters on Saturday called the conflict "a guerrilla war".
"This is our own war. This is war for the survival of the country," Reuters news agency quoted him as saying.
Our correspondent says Sunday's curfew is especially aimed at the residents of the towns of Kambar and Raheemabad.
They have been blaming both sides for the violence, he says, as the military continues to bombard the area while the Taleban reportedly prevents people from fleeing.
One Mingora resident was quoted by Reuters saying he had not been able to escape during an earlier curfew.
"We are feeling so helpless, we want to go but can't," said Sallahudin Khan.
"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."
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