Sri Lanka's military says more than 10-thousand civilians have fled from the country's northern war zone since Wednesday.
The defense ministry issued a statement Sunday saying that most of those civilians fled to Kilinochchi, while a group of 139 people fled to Jaffna.
The ministry added that Sri Lankan officials are providing medical care, food and water at the frontlines for the fleeing civilians.
There is no way to independently confirm the reports since the war zone is sealed off to independent observers and media.
United Nations officials estimate as many as 250,000 people are trapped by the fighting. Sri Lanka's military accuses the rebels of using the civilians as human shields, but the rebels say the civilians are trapped by the ongoing military operation.
The Sri Lankan military says it destroyed two Tamil Tiger boats off the northeastern coast Sunday, killing between two and six rebels.
The Tigers did not immediately comment on the claim.
Sri Lanka's president on Saturday told Tamil Tiger rebels to surrender their weapons, saying the military had surrounded the separatists on a narrow strip of land.
Aid agencies say civilian casualties have been rising due to intense fighting during the past several weeks. The agencies also say they have been unable to get essential relief supplies to victims of the violence.
U.S. and European leaders have asked both sides to stop fighting long enough to let innocent civilians escape.
Sri Lankan officials promised U.N. Secretary-General Ban Ki-moon they would protect civilians, but they have rejected international calls for talks with the rebels.
Some information for this report was provided by AFP and AP.