Officials said the attack bore the hallmarks of previous suspected assaults by Pakistan-based militant groups, underscoring the fragility of recent efforts to revive bilateral talks between the often uneasy neighbors.
There was no immediate claim of responsibility.
Pakistan has condemned the attack and said it wanted to continue to build on the goodwill created by the impromptu meeting between Modi and Sharif last month.
An army official confirmed the death of the militant as the operation to secure the base - used by MiG-21 fighter jets and attack helicopters - stretched into a second day on Sunday. He did not elaborate.
Indian leaders had already praised the armed forces for their heroism in Saturday's 15-hour shootout, with Modi saying they did not let the "enemies of humanity" who attacked the base succeed.
But that appeared premature on Sunday, as the operation resumed to secure the air base in northwestern Punjab state that sprawls across an estimated 14 square km and lies just 25 km (16 miles) from the border with historic rival Pakistan.
Outside the base, rumours had circulated all morning that more gunmen were still active after Home Minister Rajnath Singh announced on Saturday that five terrorists had been "neutralised". The official body count was only four at the time.
Military trucks were seen entering and exiting the walled compound, including a demining vehicle. Dozens of security guards continued their vigil, while protesters shouted slogans and burned a Pakistani flag nearby.
One of the Indian security men killed in the attack was Subedar Fateh Singh, who won gold and silver medals in the first Commonwealth Shooting Championships held in 1995, the National Rifle Association of India said.