The army cflaimed to have killed at lest 41 Tamil Tigers, while the separatists claimed to have killed 12 soldiers in the latest engagement.
Two weeks ago, the army said it was within artillery distance of Kilinochchi, the regional capital within the Tamil territory.
War of attrition
Damien Kingsbury, an international relations professor from Deakin University, Australia, told Al Jazeera: "What is now important is that the Tamil Tigers are now surrounded and the government forces are closing in from the east towards Kilinochchi, so they are getting very close to the Tamil Tigers' headquarters.
"The Tigers are very well resourced and can hold out for quite a period of time. Kilinochchi is surrounded by minefields.
"Having said that, the Tamil Tigers have lost Kilinochchi in the past, in the 1990s, and they regained it. Whilst the loss of Kilinochchi will be very significant, this doesn't mean there will be an end.
"The Tigers will continue to exist and the best the government can hope for is that they just resort to guerrilla tactics rather than fighting as a standing army.
"This is going to turn into a war of attrition. In the past, the government has not been able to sustain that."
In January, the government abandoned a truce both sides had largely ignored.
Three-quarters of Sri Lanka's 21 million population are Sinhalese, and have led every government since independence from Britain in 1948. The Tamils argue that they are a marginalised minority.