Pakistan's army said essential services were being restored to the city.
The International Red Cross said it was "gravely concerned" by the humanitarian situation in Swat.
Water and electricity were not available, there was no fuel for generators, most medical facilities had stopped operating and food was scarce, it said.
The fighting has reduced large parts of Mingora to rubble
"The people of Swat need greater humanitarian protection and assistance immediately," said Pascal Cuttat, head of the organisation's delegation in Pakistan.
Fawad Hussein, of the United Nations office for the co-ordination of humanitarian affairs, said:
"Since there is no electricity supply, the wells are not working. People are forced to use alternative water sources, which is causing water-borne diseases. There is no electricity in any of the health facilities."
Some 2.5 million people have fled their homes since military operations began in Swat more than a month ago.
Earlier, the Pakistani Defence Minister, Syed Athar Ali, told a meeting of Asian nations in Singapore that only "5% to 10% of the job" of clearing the Taliban from the Swat valley remained.
Syed Athar Ali said the Swat operations had 'almost met complete success'
But an army spokesman said it was not possible to predict when the military operation would be completed.
Meanwhile, 40 militants were killed in an attack on a Pakistani army base near the Afghan border, officials said.
Officials said four soldiers were also killed in an eight-hour gun battle at the camp in South Waziristan, a Taliban stronghold.
"Militants came in force and attacked a paramilitary camp and fighting lasted for eight hours," an intelligence official in the region told Reuters news agency.
The army has said it will pursue "hardcore" rebels after recapturing Mingora, the main town in Swat.
Mingora was home to 300,000 people before the fighting began.
"The main cities in the Swat valley stand clear today. The operation is being conducted in the countryside to the right and left of the valley and to the North... so the operation is ongoing and it will take a little more time," army spokesman Maj Gen Athar Abbas told the BBC.
But while Maj Gen Abbas said the remaining militants were being hunted down, he could not confirm when the army's operation in the area would be complete.
"It's difficult to give a timeline because this is an elusive enemy that has strongholds in the countryside," he said.
The US is giving full backing to the Pakistani operations, which are linked to its own offensive against the Taliban in Afghanistan.
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