The Tamil Tigers were reported to have launched new attacks on Monday in the Trincomalee area in the east of the country to try to make up for lost ground in the northern Jaffna peninsula.
In a statement late on Sunday, the Sri Lankan Defence Ministry said that troops - backed by ground attack aircraft and navy gunboats - had advanced three kilometres into Tiger-held territory in the Jaffna peninsula.
The defence ministry said 70 to 75 rebels had been killed in the fighting.
It said 12 armed forces personnel were killed and 32 injured.
The BBC's Alastair Lawson, who is in Jaffna, says helicopter gunships flew low over Jaffna town throughout Sunday as they fired missiles at rebel positions.
At the same time, MiG aircraft joined in the offensive and the army's heavy artillery fired deafening salvos.
Counter-offensives
However, our correspondent says that western military analysts point out that the Tamil Tigers have proved themselves adept on countless occasions in the past at launching sudden counter-offensives.
They say that any advances made by government troops on the ground are certain to be fiercely resisted, especially because rebel positions are well defended by mines and mortar fire.
There are reports that the army is close to capturing the strategically important town of Navatkuli, which has an important bridgehead.
If the reports are true, it means that some rebels are in danger of being cut off.
Appeal to halt
Meanwhile, the Bishop of Jaffna, Thomas Savandaranayagam, has urged both sides in the conflict to stop fighting during the election campaign and refrain from indiscriminate shelling.
The bishop says that a shell recently exploded in the precincts of his church as a group of more than 20 children were playing cricket.
He says it was miracle that no-one was injured.