The Pakistani military said on Monday that it had captured and killed a number of Taliban fighters in the city as it secured eight major road intersections.
Al Jazeera's Mike Hanna, reporting from Islamabad, said military officials had told him they would take complete control of the city within 10 days.
"They have said it is [using] 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.
"The operation may be a little slow to avoid civilian casualties, damage and destruction to property," Major-General Athar Abbas, a military spokesman, said.
"There are also improvised explosive devices planted in Mingora, and we have to clear these as well.
Abbas said that the Taliban's stated concern for the people of Mingora was simply a "ploy" to allow their fighters to escape.
"They are now remembering the civilians whom they used to behead and decapitate," he told the Associted Press news agency.
Meanwhile, six Taliban fighters were killed in an explosion in the town of Kabal, west of Mingora, a Pakistani military spokesman said.
Pakistani officials have said that almost 1,160 Taliban fighters and 69 soldiers have died since April 26, but the tolls cannot be independently verified.
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 provide 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.