"We have relaunched the operation and called in additional troops," said Sibtain Rizvi, spokesman for the Rangers paramilitary force, adding that one police officer had been injured in the firing.
An AFP reporter at the scene said gunshots could be heard inside the airport and that rangers and elite commandos were rushing inside.
The initial assault at the Jinnah International Airport began late Sunday and raged until dawn, when the military said that all 10 militants had been killed.
Equipped with suicide vests, grenades and rocket launchers, they had battled security forces in one of the most brazen attacks in years in Pakistan's biggest city. Among the 14 victims were security personnel and four airport workers.