The government says it has set up temporary shelters in the Vavuniya area, south of the fighting, where food and water will be provided.
Human rights groups have raised concerns for the safety of people living under siege in the shrinking territory.
New York-based Human Rights Watch accused the separatists of preventing people from fleeing, while the Tigers say they are protecting civilians who voluntarily move with them.
Meanwhile, at least two people were killed and 11 others injured in a roadside bomb attack in eastern Sri Lanka.
The Tamil Tigers were suspected of being responsible for Wednesday's blast, police officials said.
The explosion occurred in the town of Batticaloa, about 300km east of Colombo, the Sri Lankan capital.
A policemen and another civilian were killed in the blast when a bomb planted on a bicycle went off.
Eleven civilians, including six children, were also injured, according to police officials.
The separatists could not be reached for comment.
The attack came a day after government forces killed about 16 Tiger fighters in a naval attack near Mullativu, the fighters' last base, off the northeastern coast of the country.