The fighting, which involved artillery, mortars and small arms fire, shook the Vavuniya region just south of the rebels' mini state in the north throughout the day Wednesday, said Brig. Udaya Nanayakkara, a military spokesman.
Rebel spokesman Rasiah Ilanthirayan said no battles took place in the area.
"There were no such clashes in Vavuniya. I think they are dreaming," Ilanthirayan said by telephone from the rebels' northern headquarters.
It was not possible to independently verify the claims because the area is restricted.
The battles came amid a major escalation in fighting along the front lines in the north in recent weeks and followed the government's successful fight to oust the Tigers' from the eastern province earlier this year.
The new fighting was an effort by the rebels to reassert themselves - and to keep up morale - after that defeat, Nanayakkara said.
"They are cornered into one area ... so they want to retain that territory," he said. "(Also,) to satisfy their own cadres, they are attacking."
The fighting Wednesday began in the early morning in several places along the front lines as the rebels tried to breach the government's defenses, he said. The government retaliated, he said.
In addition to those killed, five soldiers were injured, he said.
While denying that fighting ever occurred, Ilanthirayan said another fight erupted Wednesday in the nearby Mannar when the guerrillas repelled a three-pronged attempt by government troops to advance into rebel territory. He did not give details of casualties and the military did not immediately comment on the report.
The Tamil Tigers have been fighting since 1983 to establish an independent state for ethnic minority Tamils in the island country's north and east, following decades of discrimination under governments dominated by the Sinhalese majority.
The separatist group, listed as a terror organization by the United States and European Union, has been blamed for 240 suicide bombings and hundreds of other attacks.
Soldiers in the government-controlled Jaffna Peninsula in northern Sri Lanka uncovered on Wednesday four suicide vests amid a buried stockpile of ammunition, Nanayakkara said.
Turkey has found itself in a circle of countries subject to US and European sanctions. Are they dangerous for Ankara? What is Turkey going to do in response?