More than 200 people have died in the past month as violence has worsened, raising fears that a 20-year civil war might resume. Both sides say they want talks, but most analysts are sceptical.
Naval sources said patrol boats were fired on by apparent Sea Tiger craft off the northwestern Mannar district. The navy returned fire and a suspected Black Tiger suicide boat exploded. Naval sources said they then called for air support.
Palitha Kohona, the head of the government's so-called peace secretariat, said: "There were two [rebel] boats. One was destroyed by the navy, one was destroyed by the air force.
"The people who got out of the second boat are now on land, and are being engaged by ground forces."
The air attack was the first of its kind in more than a week. The government mounted two days of bombing raids on rebel positions in the northeast last week after a suicide attack on army headquarters.
The Liberation Tigers of Tamil Eelam, whose fight for a Tamil homeland has killed more than 64,000 on both sides, had threatened to retaliate if there were any new attacks on them.
The government says it still hopes that talks can take place with the rebels next week in Geneva, but the rebels pulled out of talks indefinitely last month and the two sides cannot agree even the transport of eastern rebel leaders to a pre-talks meeting.