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Troops have poured into a strip of land along Myanmar's border with Bangladesh that is largely home to the stateless Muslim Rohingya minority since a series of coordinated and deadly attacks on police border posts last month.
Up to 30,000 Rohingya have been forced to flee their homes according to the United Nations, which is urging Bangladesh to open its border to them.
It said the foreign ministry had summoned the Myanmar ambassador late Wednesday to express "deep concern" at the humanitarian situation in western Rakhine state.
"Despite our border guards' sincere effort to prevent the influx, thousands of distressed Myanmar citizens including women, children and elderly people continue to cross (the) border in to Bangladesh," it said.
"Thousands more have been reported to be gathering at the border crossing," it said, calling for "urgent appropriate measures so that Muslim minorities... are not forced to seek shelter across the border."
Many of those seeking refuge in Bangladesh say they have walked for days and used rickety boats to cross into the neighbouring country, where hundreds of thousands of registered Rohingya refugees have been living for decades.
Since the latest violence flared up, Bangladesh's secular government has been under intense pressure to open its border to prevent a humanitarian disaster.
Instead, Bangladesh border guards have intensified patrols and coast guards have deployed extra ships. Officials say they have stopped around a thousand Rohingya at the border since Monday.
Farmer Deen Mohammad was among the thousands who evaded the patrols, sneaking into the Bangladeshi border town of Teknaf four days ago with his wife, two of their children and three other families.
"They (Myanmar's military) took my two boys, aged nine and 12 when they entered my village. I don't know what happened to them," Mohammad, 50, told AFP.
"They took women in rooms and then locked them from inside. Up to 50 women and girls of our village were tortured and raped."
Mohammad said houses in his village were burned, echoing similar testimony from other recent arrivals.
The Myanmar military has denied burning villages, but Human Rights Watch said Monday that by using satellite imagery it had identified 820 more structures destroyed in five Rohingya villages between November 10-18.