"They have said it is house-to-house operations, moving very slowly from the outskirts of the city into the core."
Many of the 300,000 people who live in Mingora fled after the military began its offensive in North West Frontier Province (NWFP) several weeks ago.
But the onset of urban warfare has increased concerns for the remaining 10,000 to 20,000 civilians that are believed to remain trapped in the city, with dwindling supplies of food and no access to medical care.
Muslim Khan, a Taliban spokesman, said late on Sunday that Taliban fighters would not attack the army in Mingora to avoid civilian casualties.
"We have seen when the army retaliate for our attacks they always kill civilians ... We do not want that," he told The Associated Press news agency.
But Khan denied that a ceasefire had been delared and said Taliban fighters would remain in the city.
"This is a long war and we will fight it strategically," he said.
"We will continue fighting until an Islamic system is enforced."
The military has already ruled out halting the fighting in Swat and on Monday said that Khan's announcement showed that the fighters were "staring defeat in the face".
A Pakistani military spokesman said that six Taliban fighters had been killed in an explosion in the town of Kabal, 20km west of Mingora.
"They were trying to plant a bomb outside a mosque but it exploded on them," he told the AFP news agency.
"The dead bodies of six armed militants are still lying near the mosque."
Pakistani officials have said that almost 1,160 Taliban fighters and 69 soldiers have died since April 26, but those tolls cannot be confirmed independently.
There has been no official word on civilian casualties, but more than 2.3 million people have left their homes because of the conflict.
Qamar Zaman Kaira, Pakistan's information minister, said on Monday that the country would at least $1bn to help resettle the displaced and rebuild the devastated areas.
"To send them back home, we have started initial satellite surveys for the rehabilitation of their homes, business and cultivatable lands," he said.