The fighting Sunday came amid an escalation in violence between the two sides along the front lines of the Tamil Tigers' de facto state in parts of the north.
In one battle near Mannar, just south of rebel-held territory, six insurgents were killed late Sunday morning, the military said in a statement. A seventh was killed in a nearby confrontation in the afternoon, the military said.
The soldier was killed in another battle in the same area, according to the statement.
The military also accused the rebels of killing a Tamil youth Sunday in the Jaffna peninsula, a violence-wracked area north of rebel territory that is under government control.
Rebel spokesman Rasiah Ilanthirayan could not immediately be reached for comment.
Each side in the conflict routinely exaggerates the other side's casualties and plays down its own. Independent verification is unavailable because the battle area is restricted.
The Tamil Tiger rebels have fought since 1983 to create an independent homeland for ethnic minority Tamils after decades of discrimination under governments controlled by the Sinhalese majority.
More than 70,000 people have been killed in the conflict.