But they say a soldier who was captured will be tried by a rebel court.
The clash, in the eastern Batticaloa district, was the bloodiest single incident since mid-June.
Meanwhile the government says that the latest fighting will not prevent it from abiding by a ceasefire signed with the rebels four years ago.
"So far... we are going to honour the cease-fire," chief government spokesman Keheliya Rambukwella told The Associated Press.
He was responding to rebel claims that the clashes suggested the country was heading back to a full-scale civil conflict.
"We are going to exercise restraint, as we sincerely believe that war is not a solution," Mr Rambukwella said.
The violence has raised fears of a return to all-out war in Sri Lanka
The rebels say that a soldier they captured in Friday's fighting is being treated by medics.
"The captured soldier is injured and is being treated at a Tiger hospital," Daya Mohan, head of the rebel political wing in the eastern district of Batticaloa, told the Reuters news agency by telephone.
"He will not be released. He will be produced in our courts."
The Tamil Tigers say fighting broke out near Batticaloa when some 60 government soldiers entered rebel-held areas and were surrounded by 200 Tigers.
The BBC's Dumeetha Luthra in Colombo says the figures are impossible to verify and that the fighting was in an area where the dividing lines are ill-defined and porous.
The Sri Lankan military denies going into Tiger areas.
It says the fighting started when rebels fired on a patrol close to an army camp.
The government says a flawed peace is better than war
Nordic ceasefire monitors said dozens of government troopshad entered an area which is generally controlled by the Tamil Tigers.
The Sri Lanka Monitoring Mission (SLMM) spokesman, Thorfinnur Omarsson, said there had been a cease-fire violation. But he did not specify which side was responsible.
A Sri Lankan sailor was also shot on Friday near the eastern town Trincomalee.
Truce in peril
Violence has spiralled in Sri Lanka in recent months, claiming about 700 lives and undermining a 2002 truce.
The rebels and the government say they still stand by the truce deal - but with rising unrest, the peace exists only on paper, correspondents say.
Many victims of the violence have been civilians and members of the security forces.
Many Tamil civilians have also been killed - by the security forces or affiliated paramilitary units, the rebels allege. Others blame some of those deaths on the rebels or other armed groups.
More than 60,000 people have died in Sri Lanka since the rebels began their fight for independence for minority Tamils in the 1970s.Güncelleme Tarihi: 20 Eylül 2018, 18:16