The statement did not however go as far as the quartet of international backers - the US, EU, Japan and Norway - which earlier called on the LTTE to negotiate terms for surrender with the government.
|The army's advances come as the country marks its independence day [AFP]
"There remains probably only a short period of time before the LTTE loses control of all areas in the north," a joint statement said.
"The LTTE and the government of Sri Lanka should recognise that further loss of life - of civilians and combatants - will serve no cause."
The four also urged the Tamil Tiger leadership to renounce violence, accept a government offer of amnesty and participate "as a political party in a process to achieve a just and lasting political solution".
The call for surrender came as the Sri Lankan army said it captured the last remaining LTTE-controlled airstrip, effectively grounding the group's tiny air force.
Military officials said the two kilometre long runway was the last of seven that had been under Tiger control. LTTE officials have not yet made any comment on the military's claim.
The LTTE are believed to have only three or four light aircraft, which they used for a few raids on military bases and in the capital Colombo, including once for a high-profile attack on the international airport.
But with their territory shrinking, they have had little opportunity to use even those aircraft.
The capture of the airstrip came a day before celebrations marking the country's 61st anniversary of independence, which the government had hoped to mark with a total defeat of the LTTE.
In comments marking independence day, Mahinda Rajapaksa, the Sri Lankan president, said the country's armed forces were close to ending more than a quarter of a century of civil war.
'Elimination of terror'
"The strongholds of terror once believed to be invincible ... have fallen in rapid succession, bringing the final elimination of terror from our motherland and the dawn of true freedom to all our people well within our reach," Rajapaksa said in a statement.
The LTTE are now pushed into a 300-square-kilometre slice of coastal area, squeezed by an increasingly confident Sri Lankan army and the navy.
On Sunday, aid agencies said some 250,000 civilians were trapped in areas where heavy fighting was raging, with dozens killed and hundreds injured.
The government has put the number of trapped civilians at about 120,000.
It is unclear as to how many people have managed to flee the area.
The LTTE have been fighting government forces since 1983, alleging marginalisation by Sri Lanka's Sinhalese majority.
The group is seeking a separate homeland for ethnic Tamils in the north and east of the country.
More than 70,000 people have been killed in the civil war.