The pro-Tiger Tamilnet.com website said forces of the Liberation Tigers of Tamil Eelam were advancing on positions held by those loyal to the renegade regional commander V Muralitharan, and there were casualties on both sides.
This is the most serious conflict since a ceasefire halted the island's civil war more than two years ago, a military spokesman said, adding it was not involved in the fighting.
The fighting complicates efforts by the country's newly elected government to try to put back on track a stalled peace process with the Liberation Tigers of Tamil Eelam (LTTE).
The main LTTE group and a faction led by the breakaway commander Karuna had exchanged mortar and machine gun fire across the river Verugal just south of the port of Trincomalee, about 240km northeast of Colombo.
"There was intermittent heavy weapons fire," he said.
"There was intermittent heavy weapons fire"
Sri Lankan military
It is not known which side started the fighting, but the LTTE vowed last month "to get rid of Karuna from our soil".
Karuna - the nom de guerre of eastern commander V Muralitharan - broke from the LTTE, saying eastern Tamils had been mistreated by the rebel movement, which is based in and controls a large jungle area in northern Sri Lanka.
The LTTE, which was previously known for its strict discipline and has a history of showing no tolerance of internal challenges, says Karuna left to evade charges he had stolen money from the rebels.
Trincomalee residents said the fighting continued. "You can hear the weapons," said one.
The rebels have been fighting for a separate state in the north and east of the island for two decades and the split with Karuna is the worst internal threat to the LTTE in that time.
Karuna is estimated to have the support of more than 6000 of the LTTE's 15,000 fighters.