The UN refugee agency (UNHCR) and Pakistani officials say that about half a million people have been displaced in the last few days since the Pakistani government launched a major offensive against the Taliban.
Another 500,000 people had reportedly been displaced by sustained violence in the region over the last few months, bringing the total number of displaced people to a million.
Antonia Paradela, a spokeswoman for Unicef, the UN children's rights organisation, said aid agencies would need more funding to cope with the influx of refugees.
"We need urgently more funds - for example Unicef needs at least $10m to continue helping the previous group of displaced families, which is more than half a million people," she told Al Jazeera.
"We're talking now more than 200,000 - and more [are] on the move."
The crisis has been intensified by other aid groups halting their work in the face of the fighting.
"A week ago we had to suspend our services due to growing insecurity which has left large numbers of the population without the necessary medical care at a time of dire crisis," Chris Lockyear, the Doctors without Borders' head of mission in Pakistan, told Al Jazeera.
"We would like to go back ... but at the moment we are finding the security is not even allowing us to evacuate patients to safer areas for treatment," he said.
"The situation in Swat has been dire for a number of months now. Over the last 12 months our ambulance service has been used 1,300 times for critical cases.
"There are critical cases located in hospitals in private homes with doctors and other medical staff who are running out of supplies."
The fighting has prompted the abandonment of a peace deal, agreed in February, between the government and the Taliban.
The pact, brokered by Sufi Muhammad, a local religious leader, allowed for the enforcement of the Taliban's strict interpretation of sharia, or Islamic law, across Malakand division - which includes Swat valley - in return for peace.
The deal had been criticised both at home and abroad and its critics, especially in the US, have welcomed the government's offensive.
During a visit to Washington, Asif Ali Zardari, Pakistan's president, pledged an all-out war against the Taliban fighters.
"This is an offensive - this is war. If they kill our soldiers, then we do the same," Zardari told America's PBS public television.
Zardari was in Washington for talks with Barack Obama, the US president, and Hamid Karzai, the Afghan president.
For his part, Obama pledged a "lasting commitment" to both Pakistan and Afghanistan, where the US is fighting Taliban forces.
'On the run'
Up to 15,000 members of the security forces have been deployed in Swat, located in Pakistan's North West Frontier Province (NWFP).
The military says it has killed scores of fighters and claims to be beating back the Taliban.
"They are on the run," the army said in a statement on Saturday.
A later statement said that helicopter gunships had attacked hideouts near Mingora, Swat's main town, and killed 15 fighters.
It said an estimated 30 to 40 more died in clashes in more than a half-dozen other locations.
People fleeing the area have also accused the military of killing civilians in its bombardment.