Bangladesh has summoned the ambassador of Myanmar to express "deep concern" at a military operation that has forced thousands of minority Rohingya Muslims to flee border villages.
The foreign ministry said "desperate people" were entering from its neighbour, seeking safety and shelter.
Bangladesh has stepped up border patrols and sent many Rohingya back.
Myanmar denies reports that its soldiers have burned down villages and killed those who return.
In a statement, Bangladesh's foreign ministry said it had asked Myanmar - formerly known as Burma - to "ensure the integrity of its border" and to stop the influx of people from 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 into Bangladesh," it said.
"Thousands more have been reported to be gathering at the border crossing."
On Tuesday, Bangladeshi authorities said they had sent 20 boat-loads of Rohingya Muslims - about 150 people - back to Myanmar in an effort to stop the influx.
The Rohingya, who number about one million, are seen by Rakhine's Buddhist majority as illegal migrants from Bangladesh.
They are denied citizenship by the Myanmar government despite many having lived there for generations.
Bangladesh has also been unwilling to accept them.
Myanmar launched a large security operation last month after nine police officers were killed in attacks on border posts in Maungdaw. Some government officials blamed a militant Rohingya group for the attack.
Earlier this week, Human Rights Watch released satellite images which it said showed that hundreds of homes had been razed in Rohingya villages over the past six weeks.
Myanmar denied the claim, saying that the Rohingya were setting fire to their own homes to attract international attention.
Some Rohingya who have arrived in Bangladesh say women are being raped, men killed and homes burned. Myanmar denies this.
Reports cannot be independently verified as the government blocks international journalists and aid workers from the area.
On Wednesday, police in the Bangladeshi border town of Cox's Bazar said they had detained about 70 Rohingya and would return them to Myanmar.
"We nabbed them after they illegally trespassed (into Bangladesh). They will be pushed back," local police chief Shyamol Kumar Nath told AFP news agency.
A Rohingya community leader, speaking on condition of anonymity, told AFP that anyone sent back could be killed.
"We have information the Myanmar army is killing those (Rohingya) people who are being pushed back from Bangladesh," he said.
"The army has burned down their villages to ashes and killed their relatives."