The rebel radio station, the Voice of Tigers, said the soldier was shot by a female combat unit when he tried to throw a hand grenade at rebel positions.
However, Scandinavian monitoring team in the area said there were no signs of a grenade attack, and the incident was being investigated.
The army solider is the second to be killed since the rebels and the government agreed the ceasefire last year.
Tensions between the two side rose in the past week after clashes in Jaffna and the interception by Sri Lanka's navy of a rebel boat smuggling weapons.
Sri Lanka's biggest donors, Japan and the United States, have already voiced serious concerns about the stability of the county's fragile peace process.
'Matter under investigation'
After Saturday's incident, the Tamil rebels said the soldier's body was being given to the Red Cross who would return it to the government forces.
Sri Lanka's defence ministry said it had ordered an investigation into the incident.
The Scandinavian monitors said they could not confirm rebels' claims of a grenade attack, but said the soldier appeared to be carrying a grenade with him.
"Two of our monitors went to the spot and have taken photographs of the body," the spokesman of the Sri Lanka Monitoring Mission, Teitur Torkelsson, was quoted as saying by the AFP news agency.
"The matter is still under investigation," he added.
The incident comes just days before as the government and rebels from Liberation Tigers of Tamil Eelam (LTTE) are preparing to mark the anniversary of the truce.
Norway brokered the deal in Sri Lanka on 23 February 2002 and has been mediating talks to end the war that has killed 64,000 since 1983.
Five rounds of peace talks have been held in an attempt to end the conflict.