Sri Lanka's army has broken through the "last major defences" of the Liberation Tigers of Tamil Eelam (LTTE) near their de facto capital of Kilinochchi, according to the defence ministry.
At least 19 Tamil Tiger bunkers were also captured along a two-kilometre line during Saturday's fighting in the north of the island, the statement said.
"Army's 57 division troops yesterday pierced the LTTE-built earth bund in Akkarayankulam, the terrorists' last major defence south of Kilinochchi," the defence ministry said on Sunday.
The Sri Lankan military statement did not detail casualties from the fighting but it said that the Tamil Tigers "suffered significant attrition in terms man and material".
"Several soldiers made their ultimate sacrifice for the nation while many others suffered injuries during this battle," the defence ministry added.
The LTTE, which has been fighting for an independent state for ethnic Tamils in the north and east of the island since 1972, did not immediately comment on the military's claims.
It is impossible to independently verify competing claims by the two sides as the region, where the army has been pursuing an offensive against Tamil Tigers for more than a year, is closed to most journalists.
The military claimed that Tamil Tiger fighters had used "poisonous gas attacks" in an attempt to halt the advance of government forces. Military sources told the AFP news agency that a type of tear gas commonly used in riot control had been used.
"However, troops withstood the chemical attack and beat off the terrorists," the ministry said.
Three weeks ago, the military announced that it was within striking distance of Kilinochchi, the loss of which would be a major blow to the Tamil Tigers who are thought to have been significantly weakend by the sustained military offensive.
The fighting took place as Mahinda Rajapaksa, Sri Lanka's president, sought to reassure Manmohan Singh, India's prime minister, that the military was trying to minimise civilian casualties, a foreign ministry statement said.
Nearly 40 politicians from the ruling Dravida Munnettra Kazhagam (DMK) party in India's Tamil Nadu state submitted their resignations on Friday in an attempt to put pressure on the government to intervene in Sri Lanka.
Tamil Nadu is home to about 55 million Tamils who have ancestral links with the Tamils in Sri Lanka.
The DMK is allied to Singh's Congress party and it gave the government two weeks to do something or face being brought down.
India sent peacekeepers to Sri Lanka in 1987, only to withdraw them after losing more than 1,000 men in battle.