Military says 15 Tamil Tiger fighters and six soldiers died in latest offensive.
The pro-Tigers Tamilnet.com website said a farmer was shot dead by unidentified armed men late on Monday in the eastern town of Akkaraipattu.
There was no independent confirmation of how many people were killed in the fighting or what had happened.
Military analysts say both sides tend to exaggerate enemy losses and play down their own.
The Tigers say they have been isolated from the international community since a 2002 ceasefire pact broke down early last year, and called on foreign governments to support the idea of sovereignty for Tamils and to give them a forum to voice their views.
“The government of Sri Lanka must end its deceptions, halt its military oppression, ethnic cleansing and serious human rights violations”
Statement from the Liberation Tigers of Tamil Eelam
Their appeal came hours before Mahinda Rajapaksa, Sri Lanka’s president, was due to address the UN General Assembly in New York.
In a statement released early on Tuesday, the Tigers said: “The government of Sri Lanka must end its deceptions, halt its military oppression, ethnic cleansing and serious human rights violations.
“(It must) accept the aspirations of the Tamil people and come forward to find a resolution that is based on the right to self-determination of the Tamil people.
The government has repeatedly offered to hold peace talks with the Tigers, but has also vowed to wipe out their military capability and has launched repeated offensives into Tiger-held territory – which military analysts say sets the stage for more war.
Around 5,000 people have been killed in fighting between the military and the LTTE since early 2006. Fighting is now focused on the north after troops this year drove the Tigers from eastern areas they controlled under the terms of a now-tattered ceasefire pact.
In all, nearly 70,000 people have been killed and hundreds of thousands displaced since the war erupted in 1983, and few see a clear winner on the horizon.