"Our planes have attacked the air facility and a storage in Palaly," Ilanthirayan said by telephone from the rebel stronghold of Kilinochchi.
He said the pilots saw flames after dropping their bombs.
"It may have caused damage to their [military] command chain located within the base."
Initially, the Sri Lankan defence forces denied the air raid.
"We are made to understand that they [Tigers] had attacked with artillery and we have not got any reports on casualties," Group Captain Ajantha Silva, a Sri Lanka's air force spokesman, said.
But Fonseka said the military switched off lights, rolled out heavy guns and opened fire when attacked from air.
"Troops at the forward defence lines saw them [Tiger aircraft] coming and alerted the Palaly base, and they used all their resources to direct fire at the aircraft," he said.
Military sources said six troopers were killed and six wounded in the Tiger air attack.
On March 26, at least one rebel propeller plane bombed a Sri Lankan air force base outside the capital, Colombo, in the separatists' first air strike since they started their campaign for a homeland for the country's Tamil minority in 1983.
Three soldiers were killed in that attack and 16 were wounded, but no aircraft on the ground were damaged.
The aircraft then flew for more than an hour to return to rebel-held territory in the island's north without being challenged either by military aircraft or troops on the ground.
Since then, the Sri Lankan military has acquired night-flying capabilities and said it has bombed several suspected Tiger targets, including naval assets, communications facilities and training camps.
Sri Lanka's military said it had stepped up its air defences since that attack and set up a telephone hotline in case citizens notice any unidentified aircraft.
The battle for an independent Tamil state has left more than 60,000 people dead.
Hours before Tuesday's attack, a roadside bomb killed three people and wounded 35 in Vavuniya, which is next to a separatist-held area, the defence ministry said.