The country, already home to a Rohingya refugee population estimated at 300,000, turned away more migrants on Thursday and has sealed its 200-kilometre border with Myanmar.
At least 17 boats carrying nearly 700 Rohingya have been turned back on the Naf river that separates the countries since Monday.
"Our position on the Myanmar refugee issue remains the same," Bangladesh foreign ministry spokesman Masud Mahmood told AFP.
The United States on Wednesday urged Bangladesh to allow in the Rohingya, described by the United Nations as one of the world's most persecuted minorities.
"We are concerned that Bangladeshi authorities appear to have intercepted and turned back persons fleeing the ethnic and religious violence in Burma," State Department spokeswoman Victoria Nuland said, using Myanmar's former name.
Nuland said the US had urged Bangladesh "to respect its international obligations under the relevant refugee conventions and to continue its longstanding policy of non-refoulement of refugees."
Non-refoulement refers to a principle of international law that forbids turning over a victim of persecution to his or her persecutor.
The UN Refugee Agency and New York-based Human Rights Watch have also called on Dhaka to open its border.
Bangladesh Foreign Minister Dipu Moni has said the country will not allow any "trans-boundary spill-over" from Myanmar.
"It is not in our interest that new refugees come from Myanmar," Moni said on Tuesday. "The entry of refugees from Myanmar has impacted on Bangladesh's social, environmental and law-and-order situation."
The violence in Rakhine state, where the majority of Myanmar's 800,000 Rohingya live, left at least 38 people dead this month.
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