As airport security forces took up positions, many of them combed out of the training facility and moved toward the edges of the slum. Several television journalists also tried to move in the same direction as bursts of gunfire echoed in the background.
An airport security official, Col. Tahir Ali, played down the violence, saying that only two attackers engaged the security guards with gunfire.
"It was not an attack as such. They came and fired," the official said. "We cannot take any risk. We will try to contain them immediately."
He said a search was underway for the suspects in the slums near the training facility, and added that no one was injured in the gunbattle, in which the insurgents came on a motorbike before fleeing by foot after exchanging fire.
Omar Khorasani, a Taliban official, said on his Twitter account that his group carried out Tuesday's attack. "We are back to ASF academy. Allah is Great. Allah is Great. Allah is Great," the Twitter message said.
The escalating conflict came as peace talks between the Taliban and the Pakistani government have broken down, leading the Pakistani military to stage a series of raids on insurgent hideouts.
Pakistani military officials did not immediately confirm that Tuesday's airstrikes were in retaliation for the weekend raid on the airport. Security officials said at least 25 militants had been killed in the raids.
In Sunday's airport attack, a squad of militant commandos came equipped with food, water and ammunition, apparently in preparation for a long siege. Government officials said they may have been trying to hijack a commercial airliner, blow up an oil depot or destroy airplanes on the tarmac.
But the 10 attackers were dead five hours later, shot by soldiers or blown up by their own suicide vests. The Taliban subsequently claimed responsibility for Sunday's attack.
Also Tuesday, at least seven charred bodies were recovered from a cold storage area in the Karachi airport, leading to outrage and condemnation by distraught relatives, the local news media reported. On Monday, the government had declared that the airport had been cleared and was fit for resumption of flights. But the discovery of more bodies has raised questions about the extent of damage that has been reported by authorities.
The seven people, who worked for a private cargo firm, hid in the cold storage area as a battle raged between the attackers and security forces late Sunday. The cause of their deaths was still under investigation.
Shahzad Humayoon, whose brother Fareed Khan was one of the seven, said authorities had retrieved the bodies only after a protest Monday night by relatives who blocked the city's main thoroughfare, Shahrah-e-Faisal, which connects the airport to the city.