The Red Cross said its workers had tended to 4,000 people who crossed the front lines yesterday. Spokeswoman Sarasi Wijeratne said the organization was not in a position to "confirm or deny" the large number being quoted.
A pro-rebel website, meanwhile, said hundreds of civilians might have been killed in the "total chaos" that prevailed when soldiers entered the zone. It was not possible to verify any of the reports because journalists are restricted in the war zone.
UN Secretary-General Ban Ki-moon welcomed the civilians' escape but remained deeply concerned about thousands still trapped and "the potential for large-scale casualties," UN spokeswoman Marie Okabe said in New York. Ban also said aid workers must be allowed into the area to help civilians.
US State Department spokesman Robert Wood called the humanitarian situation "dire" and asked both sides to "cease this violent activity."
The UN had estimated 100,000 civilians were trapped in the zone where the rebels have been pinned down, an area that measures less than 8 square miles.
UN officials say 4,500 noncombatants have been killed over the last three months amid fierce fighting during a government offensive that has driven the rebels from their strongholds.
The military spokesman, Brigadier Udaya Nanayakkara, said soldiers broke through part of a 7-mile-long earthen barrier erected by the Tamil Tigers to seal off the small area that had been designated a "no-fire zone" and where the rebels have dug in for a final stand.
That allowed civilians to stream out toward government lines.
Video on state television Rupavahini showed dozens of men and women wading across a lagoon in neck-high water. Some people were wounded and dripping blood. Others carried children or wounded relatives on their shoulders.
A girl wept over the body of a relative who state television said was killed in a rebel suicide bombing aimed at preventing civilians from leaving.
Few possessions were carried out. Some people wore rucksacks on their backs, others held sacks on their shoulders or bulkier bags on their heads.