In all, about half a million people are expected to flee the recent fighting. They join more than 550,000 people displaced earlier from Swat and other areas because of fighting since August.
Later reports suggested there was confusion about when the curfew would be reimposed, leaving some people at risk of being caught in the fighting.
The military has issued a "shoot on sight" order for anyone found violating the curfew.
While the roads out of Swat are packed with refugees, roads leading in have been locked down by the military.
"The government wants to ensure that the Taliban cannot re-enforce their positions there," our correspondent reported.
Helicopters and warplanes targeted Taliban hideouts in Mingora, Swat's main town, and other areas in the valley, Nasir Khan, a military spokesmen in the area said.
"It's a tough battle. They're operating in small groups. They don't fight a pitched battle, but we're closing in on them, squeezing them and have cut their supply lines," he said.
He offered no information on casualty figures, but a day earlier, the army said its troops killed dozens of entrenched Taliban fighters.
In recent days the military has battled the Taliban in the area, often imposing curfews unannounced to do so.
But it lifted its curfew on the area at midnight GMT on Saturday and ordered residents out, initially giving people seven hours to leave, but later extending that period.
An all out assault on Taliban positions is expected once the residents have left.
"You can't put a time line on [an attack], but the movement of people [from the area] would clear the path for the military to bring in the boots on the ground," our correspondent said.
'War of survival'
Yousuf Raza Gilani, Pakistan's prime minister, has called the military's operations against local Taliban members a "war of the country's survival".
|Many of those fleeing Swat have
ended up in IDP camps
The fighting has prompted the abandonment of a peace deal, agreed in February, between the government and the Pakistani Taliban.
The deal, which had allowed for the enforcement of the Sharia, or Islamic law, across Malakand division, including the Swat valley, had been criticised both at home and abroad.
But while Washington has been enthusiastic about Pakistan's offensive on Taliban positions, the fighting has caused a humanitarian crisis in the North West Frontier Province - one that the local government has been unprepared to deal with.
Despite the huge influx of refugees to IDP camps in nearby Mardan, there has been little evidence of the local government's presence.
Many local government officials are thought to have gone into hiding since the collapse of the peace pact, fearing that they have become targets for the Taliban.
"The only people who have really responded to this crisis have been the international aid agencies and the local population - volunteering in the camps and opening their homes," our correspondent reported.
But there are now fears that fighting could spread closer to the camps, with reports of Taliban fighters being seen in parts of Mardan.