The army says that it is on the verge of total victory
The last remaining strip of rebel-held land on the northern Jaffna peninsula is now in government hands, the Sri Lankan administration says.
Correspondents say that taking full control after nine years is another strategic victory for the government.
The capture follows the recent fall of the town of Kilinochchi and the strategically important Elephant Pass.
Separately, the president has pledged to protect press freedom in the wake of a high-profile journalist's killing.
Last week leading newspaper editor Lasantha Wickramatunga was murdered by unknown attackers.
"Troops liberated Chundikulam, the land mass that links the Jaffna peninsula with the mainland," the defence ministry website said of the latest fighting.
There has been no comment on the claim from the Tamil Tigers.
Aid agencies are increasingly concerned over the plight of civilians
The peninsula and its capital, Jaffna, have long been regarded as the symbolic heart of their 25-year-old separatist insurgency.
Military spokesman Brig Udaya Nanayakkara said the army did not suffer any casualties in the latest action.
Independent journalists are prevented by the government from travelling to the conflict zone, so it is impossible to verify the casualty claims made by both sides.
The military says that it hopes over the coming months to crush the Tigers completely.
The Tigers have been fighting for a separate homeland for 25 years. At least 70,000 people have been killed in the insurgency.
Human rights groups such as Amnesty International meanwhile say that they are increasingly concerned about the plight of civilians in the conflict area.
The rebels are now fighting a rearguard action
In a letter to Indian Foreign Secretary Shivshankar Menon ahead of his visit to the country, Amnesty says that more than a quarter of a million people, mostly Tamils, face "immense hardship".
They say that civilians are "running out of space in the face of intensified fighting between the two sides".
"The Sri Lankan government's recent recapture of Killinochchi has meant that hundreds of thousands of people have been compressed into a smaller area and are increasingly vulnerable," the letter states.
The government said this week it was fully prepared to handle "the mass exodus of civilians" the fighting with the rebels might cause.
Amnesty has also called on the Indian foreign secretary to raise the issue of attacks on the media and press.
President Rajapaksa argues that at a time when the government is at the "very height of its popularity due to the success of the offensive against terrorism", it has "no interest in losing this public acceptance by... attacks on the media".
He insisted that the culprits in Mr Wickramatunga's death would be captured and brought to justice.
But at the same time he warned journalists to show "greater responsibility" in their reporting.
In an apparently self-penned article predicting his death published earlier this week, Mr Wickramatunga blamed the government.
In the piece entitled And Then They Came For Me, he wrote: "When finally I am killed, it will be the government that kills me."