Local police said the shelling near Trincomalee, heard by Reuters witnesses on Tuesday morning, might have been from clashes between the Tigers and a breakaway faction, Karuna, which the rebels say is government backed.
S Eilan, a local Tiger leader, said: "It is from the Sri Lankan military, we retaliated and fired shells back."
Witnesses in Trincomalee town, across the harbour from Tiger territory hit by government air strikes last week, said they had heard explosions and shooting.
The rebels have threatened military retaliations if the government resumes air strikes. Some fear that could reignite the island's two-decade civil war, which has killed more than 64,000.
Nihal Samarakoon, a police senior superintendent, said the explosions were coming from Liberation Tigers of Tamil Eelam (LTTE) territory, and that he believed renegade ex-rebels led by former eastern Tiger commander Karuna Amman were involved.
"It looks like a Karuna and LTTE clash," he said. "But there are no details."
The government had promised, at a first round of peace talks in Switzerland in February, to disarm groups in their territory, but are seen to have done nothing.
That has in turn angered the Tigers, who are said to have begun a series of attacks on the military.
The rebels, who want a homeland for Sri Lanka's Tamil minority, deny repeated ambushes on the military. Few believe them.
Both sides say they want to attend new talks, but the Tigers say they must first meet their eastern commanders. That process has become deadlocked.
The stock market rose 1.2 per cent before falling back a quarter of a per cent after news of the shelling.