Karen rebels have been fighting the Burmese authorities for decades
About 3,000 ethnic Karen villagers have reportedly fled from Burma into Thailand in recent days because of a new Burmese military offensive.
Aid groups say the refugees are from Ler Per Her camp in eastern Karen state, near where the Burmese army is reported to be attacking Karen rebels.
It is thought to be one of the largest movements of refugees across the Thai-Burma border in a decade.
Meanwhile Burma still faces pressure to halt Aung San Suu Kyi's trial.
The pro-democracy leader is charged with breaching the terms of her house arrest, a charge that could leave her in jail for up to five years.
Former Singapore Prime Minister Goh Chok Tong visited Burma on a "goodwill trip" on Monday, as international anger against the regime continued to mount.
'Largest exodus for a decade'
The Free Burma Rangers aid group said refugees began streaming out of the Ler Per Her camp on Friday and continued to arrive in Thailand throughout the weekend.
The Karen Human Rights Group, a Thai-based humanitarian group, put the number of refugees at about 3,000 - and so too did a Thai army official speaking to local media.
The Burmese government has refused to comment on these reports.
The Karen Human Rights Group said the influx was "the largest exodus from Karen state on a single occasion" since the government launched a major offensive against the Karen rebels in 1997.
The refugees are now taking shelter about 100 km (62 miles) north of Mae Sot, a Thai border town.
The rights group Christian Solidarity Worldwide and other organisations have called on the United Nations to intervene to prevent a humanitarian crisis along the border.
Rebels from the Karen National Union (KNU) have been fighting for greater autonomy from Burma's central government for more than half a century.
But the KNU is weakening under the impact of continued army offensives, as well as divisions within its ranks and with other Karen groups.
Another group, the Democratic Karen Buddhist Amy (DKBA), made a pact with the Burmese government and is reportedly now involved in the current fighting on the government side.