The rebels say the government uses fighters led by former Tiger eastern commander V Muralitharan, better known as Karuna, while "army-backed paramilitaries" attack the mainstream Liberation Tigers of Tamil Eelam (LTTE) - a charge the government denies.
"It is a very severe blow for the paramilitary groups and for the Sri Lankan army," the head of the Tiger peace secretariat, S Puleedevan, told Reuters by satellite phone from rebel territory.
Twenty Karuna fighters were killed and 15 wounded, he said.
"We have burned the camps and a lot of arms and ammunition provided by the Sri Lankan army," he added.
He said his men had come under artillery fire from nearby army camps during the attack, but were withdrawing back behind their own lines with only one Tiger fighter wounded.
The Tamil rebel group split in 2004 when Karuna, a powerful leader from the east, broke away from the northern group with about 6,000 fighters.
The uprising was then ruthlessly suppressed later by the main rebel group, but sympathy for the breakaway leader remains strong among some Tamils in the east.
An official of the breakaway group denied there had been any fatalities on Sunday.
"It is a very severe blow for the paramilitary groups and for the Sri Lankan army"
head of the Tiger peace secretariat
He said, speaking on condition of anonymity, that his group's fighters had only suffered injuries.
Talking by phone from Batticaloa, he claimed the breakaway rebels killed eight cadres from the mainstream group.
Maxi Procter, a senior police offcier in Batticaloa, confirmed for his part that there had been fighting between the two groups, but declined to give further details.
And the army denied there had been any shelling, and said all they knew was there had been fighting between Tiger and Karuna forces in jungle areas not really controlled by either side.
They have always denied knowing where the Karuna camps were, but Nordic truce monitors said the army, at best, turns a blind eye.
Karuna broke ranks with LTTE's
Prabhakaran two years ago
Analysts also say that with war still seen as very possible, the military would be unlikely to disarm Karuna despite promises at a first round of peace talks in February to stop armed groups operating from their territory.
The past three weeks have been the bloodiest since a 2002 ceasefire with more than 120 people - possibly many more - killed in suspected Tiger attacks on the military, ethnic riots, government air strikes and unsolved murders of civilians on both sides.
Peace talks due to take place in Switzerland have been indefinitely postponed because of wrangling over the transport of eastern rebel leaders to their headquarters for a pre-talks meeting.
Analysts also say that ultimately the key issue for the Tigers, whose two-decade fight for an ethnic Tamil homeland has killed more than 64,000 on both sides, was to stop Karuna.
The attacks took place near the eastern town of Welikanda, where the Tigers say Karuna fighters kidnapped several aid workers from the Tamils Rehabilitation Organisation (TRO), effectively the aid arm of the de facto Tiger state.
The head of the Tiger peace secretariat said his group had found two seized TRO vehicles inside the three Karuna camps raided, but no sign of the seven aid staff still missing.