The authorities have imposed a local police curfew in Anuradhapura to enable the military to comb the surroundings for attackers.
The area was rocked by the sound of explosions and gunfire from early morning, residents said.
The bodies of 20 Tiger attackers were found in and around the air base.
The attack on the Anuradhapura air base, 212 kilometres (130 miles) north of the capital Colombo, started around 3 a.m. Monday morning when a group of Tiger infiltrated the base.
This was followed by two Tiger light aircraft dropping two bombs on the base and escaping despite anti-aircraft fire by the defenders.
The Tigers, fighting for a separate homeland for minority Tamils in the island's north and east, are believed to have a small fleet of Czec