The army's latest declaration comes days after a lethal bombing in Lahore, which was later claimed by Taliban as revenge for the Swat operations.
Although the military has always had bases in Mingora, the city was in effect under Taliban control in recent weeks.
The army reported taking key intersections a week ago and fighting is said to have been fierce in the city which was only recently home to more than 300,000 people.
"They [the Taliban] had prepared Mingora city... with bunkers but when they realised that they were being encircled and the noose was tightening, they decided not to give a pitched battle," said Gen Abbas.
Major General Athar Abbas claims as few as 1000 militants remain in the Swat valley
But he emphasised he was only talking about Mingora and said there was "much more fight[ing]" to be done in the valley.
Work, he added, was already beginning to restore essential services to Mingora.
The city hospital was being re-opened, he said, with a team of 21 doctors and adequate medical supplies.
Gas had also been restored and some mobile generators had been provided for the water system.
It would take at least two weeks to restore the electricity network, the general said.
As the army aims to clear Taliban strongholds and supply depots in Swat's mountains, soldiers are battling militants in towns where many thousands of civilians are believed to be hiding.
The government has also advised residents to leave the town of Charbagh, a Taliban stronghold 20 miles (32km) north of Swat, in advance of an attempt by the military to move in there, AFP reported, quoting unnamed military sources.
Following the attack in Lahore, and in Peshawar a day later, Pakistan increased its reward for a Taliban chief to 50m rupees ($600,000, £372,000).
The figure is more than 10 times the original bounty for radical cleric Maulana Fazlullah - believed to be the architect of a two-year uprising in the Swat valley intended to enforce Sharia law.
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