Sri Lankan troops have entered the last town held by Tamil Tiger separatists, a government spokesman says.
"Troops of the 59th division entered Mullaittivu town a short while ago and we hope they will consolidate their hold across the town in a few hours," Keheliya Rambukwella, the government spokesman, said on Sunday.
Brigadier Udaya Nanayakkara, a Sri Lankan military spokesman, said that the fighting around Mullaittivu was heavy.
"Troops are negotiating pockets of fighting here and there," he said.
It was not possible to independently verify the government's claims, as journalists are banned from the war zone.
The military says it has made dramatic gains in recent months, pushing the Tamil Tigers, who are fighting for an independent homeland in the north and east of the island, back to a small area in the east of the country.
"It does sound ominous for the Tamil Tigers, but you have say, put in this context, perhaps Mullaittivu was not going to be the last resting place for them," Al Jazeera's Tony Birtley, reporting from the capital Colombo, said.
"It was always thought that they would flee to the jungles where they would have a much higher degree of safety and it would be harder to flush them out.
"We don't know how strong the Tamil Tigers still are, how well armed they still are, but if there is a hardcore there they can still operate from the jungle and that could cause problems for the Sri Lanka government.
"There is still the possibility and the concern that there may be some sort of counter-offensive launched soon."
The rebels took control of Mullaittivu in 1996 when they overran a military camp there, killing nearly 1,000 soldiers.
On Sunday, the military said that the retreating rebels had flooded two villages after destroying a reservoir in an attempt to stall advancing government troops.
"As the conflict lines get closer these people are becoming more and more exposed to instense fighting and are increasingly caught in the crossfire"
in Sri Lanka
Tamil Tiger fighters used explosives to destroy the walls of Kalmadukulam reservoir on Saturday, as government troops advanced on Visuamdu, in Mullaittivu district, a statement said.
Details of the welfare of villagers and the damage caused by flooding from the dam were not immediately available.
Soldiers also clashed with fighters in Chundikulam village in the same district and hours later recovered the bodies of two Tamil Tiger fighters, according to the statement.
As fighting has intensified, aid groups and diplomats have expressed fears for the safety of hundreds of thousands of civilians reportedly trapped in Tiger-held territory around Mullaittivu.
"As the conflict lines get closer these people are becoming more and more exposed to instense fighting and are increasingly caught in the crossfire," James Elder, a spokesman for the UN in Sri Lanka, told Al Jazeera.
"We are calling on the LTTE [Liberation Tigers of Tamil Eelam] to meet their international responsibilities and guarantee that the civilian population can move freely and get away from this conflict zone," he said.
The rebel-affiliated TamilNet website said that five civilians were killed on Friday and 83 wounded when the army fired artillery shells into a government-declared "safe zone" for displaced families.
A doctor in the area confirmed on Saturday that five civilians were killed in shelling.
The military denied firing into the civilian settlements and launching attacks on the "safe zone", accusing the Tigers of carrying out the assaults themselves to keep civilians out of the area.
Human rights organisations have accused the rebels of using the civilians as human shields to block the government offensive.