Matta is about 25km northwest of Mingora, while Kanju is just 2km from the outskirts of the town.
"At present intense fire engagements are taking place at the outskirts of Mingora," the military statement said on Sunday.
'On the run'
Pakistani government forces had said on Saturday that they were gathered outside Mingora, prompting speculation of an imminent assault on the town.
"I appeal to the people of Mingora and other parts which are under aggression, as soon as they get an opportunity, the curfew is relaxed, they should come out," Rehman Malik, the interior ministry chief, said.
"The militants are on the run, they will be eliminated at any cost."
The military has said that it has avoided civilian deaths as the conflict has been confined to the mountains, but an assault on Mingora would likely increase the chance of casualties.
At least 15,000 government troops are reported to be battling about 5,000 Taliban fighters in Swat valley.
Malik, speaking from the town of Mardan where some of the more than one million people displaced by the fighting are living in makeshift camps, said he hoped people would soon be able to return home.
"People wish to go back. That is what the government also wants. I cannot
give a time but we will try [to complete the operation] at the earliest," he said.
The United Nations has registered 1.17 million people displaced by the fighting since the beginning of the month, but officials believe that many more may have fled without notifying the authorities.
The military said on Sunday that troops were also making gains in the remote Peochar area, said to be the rear base of Maulana Fazlullah, a local Taliban leader.
Britain's Sunday Times newspaper reported that the military could move into Pakistan's semi-autonoumous tribal areas after the current offensive in the North West Frontier Province (NWFP).
"We're going to go into Waziristan, all these regions, with army operations," the paper quoted Asif Ali Zardari, Pakistan's president, as saying.
"Swat is just the start. It's a larger war to fight."
Beitullah Mehsud, the Pakistani-Taliban leader, is believed to be based in South Waziristan, along the border with Afghanistan.