A paramilitary spokesman said one policeman was injured in the fresh firing.
"We have relaunched the operation and called in additional troops," Sibtain Rizvi, spokesman for the Rangers paramilitary force, told the AFP news agency.
All flights to Karachi were cancelled for the day.
A separate suicide bombing at Taftan in the country's southwest killed 23 Shia pilgrims returning from Iran.
Suspicion for the airport attack had fallen on the Pakistan Taliban, who recently abandoned a ceasefire after peace talks stalled. Their gunmen and suicide bombers have been responsible for tens of thousands of deaths during a seven-year insurgency.
Abdullah Bahar Mehsud, a senior commander, said the attack was carried out to avenge the death of the group's former leader Hakimullah Mehsud in a drone strike last year.
Watch: Raw: Deadly attack on Pakistan airport
"As long as we are breathing, our attacks will be continuing till the end of our lives," he said.
Another Pakistan Taliban spokesman, Shahidullah Shahid, also confirmed the attack was to avenge the death of Hakimullah Mehsud, while dismissing the Government's recent offer of peace talks as a "tool of war".
He also promised more attacks in the future.
"Pakistan used peace talks as a tool of war, it killed hundreds of innocent tribal women and children. This is our first attack to avenge the death of Hakimullah Mehsud," he said.
"We have yet to take revenge for the deaths of hundreds of innocent tribal women and children in Pakistani air strikes.
"It's just the beginning, we have taken revenge for one, we have to take revenge for hundreds," he said.
The attack was close to the airport's old terminal, used mainly for cargo and VIP passengers. The gunmen - dressed in police uniforms, some wearing suicide vests - used rocket-propelled grenades and automatic weapons.
A security source said their target may have been an airliner which was boarding passengers.
Plumes of smoke spiralled into the air.
All flights were diverted but the main passenger terminal was successfully evacuated and most travellers were kept well away from the clashes.
Pakistani commandos get ready to enter Karachi airport terminal. Photo / AP
However, at least one plane - an Emirates flight to Dubai - was turned back from the runway as the attack unfolded. Farooq Sattar, a senior figure with the Muttahida Qaumi Movement was on board, and described how the aircraft reached the runway only to turn back as the sounds of gunfire exploded around them.
"They have told us we are safer on board and so the doors will stay shut," he said. "But this aircraft is full of fuel and so are the other planes here. If God forbid the terrorists come here then there could be a terrible fire."
Yesterday morning, Major General Asim Bajwa, the military spokesman, declared the attack over.
"Update: Area cleared. No damage to aircraft, fire visible in pics was not plane but a building, now extinguished. All vital assets intact," he said in a tweet.
A huge blast was heard after one of the gunmen wearing a suicide vest blew up after he was shot.
Initial reports indicated up to 10 gunmen had used a side entrance to attack the terminal but were prevented from reaching their target by security personnel.
Dr Seemi Jamali, who is head of the city's main Jinnah Hospital, said 11 of the bodies brought to the morgue were of airport security personnel.
Fire illuminates the sky above Karachi airport terminal. Photo / AP
Sarmad Hussain, an official with the state-run Pakistan International Airlines, told how he heard explosions and gunfire as the attack broke out. "I was working at my office when I heard big blasts - several blasts - and then there were heavy gunshots," he said, adding that he and a colleague jumped out one of the windows to get away, and his colleague broke his leg.
Hussain said he saw smoke billowing from the terminal.
Security officials said Uzbek and Chechen nationals were among the attackers.
"Three militants blew themselves up and seven were killed by security forces," Rizwan Akhtar, the regional head of the paramilitary Rangers, said in televised remarks. "The militants appear to be Uzbek."
The Islamic Movement of Uzbekistan is one of a number of foreign groups that operates from bases along the border with Afghanistan in tandem with Pakistani groups.
Security is a major concern at Pakistan's airports. The US will not allow passenger airlines to fly direct to its soil.
- additional reporting AFP, AP
