The Sri Lankan army says more than 2 000 civilians have waded across a lagoon to flee the war zone in the north-east of the country.
A senior military officer said another 2 000 people were waiting to cross into government-held areas, the BBC reported Thursday.
The reports come hours after Colombo rejected calls to stop its offensive against the cornered Tamil Tigers.
The UN Security Council has expressed "grave concern" at the "worsening humanitarian crisis" in the region.
It says about 50 000 people are trapped in the tiny coastal strip where the rebels have been cornered by the army.
A military spokesman told the BBC that unmanned aircraft had filmed more than 2 000 people wading across the lagoon which borders the fighting zone on the non-seaward side.
The Sri Lankan army's version of events cannot be independently verified and there has been no comment from the rebels.
Earlier, the UN Security Council asked the Sri Lankan government and the Tamil Tigers to ensure the safety of civilians.