UN and Chinese officials say 30,000 people fled the fighting
Burmese refugees in China's southern Yunnan province are beginning to return to Burma, China's state-controlled Xinhua news agency has reported.
The refugees are from Kokang, in northern Burma, and fled fighting with Burmese soldiers last week.
Burmese state media said the fighting was over and that the area had returned to "normalcy", but fears of further fighting remain.
China issued a rare rebuke to Burma after receiving about 30,000 refugees.
Burma said on Sunday that three days of fighting was over between its troops and rebels in the northern Shan State.
State television said 26 soldiers and eight Kokang fighters had been killed. But these numbers are low given the numbers of refugees who fled the conflict, correspondents say.
It was the first announcement from Burma on the conflict.
Analysts said the fighting was part of a drive by Burmese state forces to force autonomous rebel groups in the area to participate in elections next year, indicating further conflict is likely.
Burma's military rulers, however, said the fighting had erupted after government forces tried to rescue 39 policemen it said were being held hostage by the MNDAA, also known as the Kokang Group.
Many people are reported to have fled to avoid being conscripted as porters or soldiers by the Burmese military.
The BBC's Chris Hogg, reporting from Nansan in Yunnan province, said the border town was heavily guarded but appeared peaceful on Sunday.
Some of the men who had been fighting the Burmese army said they were outnumbered and outgunned by the government forces, adding they planned to return to Burma once they could be sure if was safe.
Foreign reporters have not been allowed access to the refugee camps.