“We have told Myanmar that they will have to take back their citizens. Provide security for them,” she said on Tuesday while speaking at a reception hosted by her party's US chapter.
More than 400,000 Muslim Rohingyas have fled across the border to Bangladesh in three weeks after a counter-insurgency offensive by Myanmar's army in the wake of militant attacks on security forces.
The UN has described Myanmar's strategy as "ethnic cleansing".
Bangladesh was already home to 400,000 Rohingya refugees before insurgents attacked 30 police outposts and an army base in the western Rakhine state on Aug 25.
Hasina, who arrived in New York on Sept 18, is scheduled to address the 72nd United Nations General Assembly on Sept 21.
Officials said the prime minister will highlight the root causes of the crisis and Bangladesh's proposals to solve it.
Over the last two days, the prime minister has urged the international community to unite for stopping violence in Myanmar in several sessions.
“What we want is to mount pressure on Myanmar, to take back their people and implement the recommendations by the Kofi Annan commission," Awami League President Hasina said at the reception at the Marriott Hotel in Manhattan.
Referring to her recent visit to the Cox's Bazar refugee camp, she said it reminded her of 1971.
The prime minister said many in the international community have asked her how Bangladesh will support the huge number of refugees.
"I had told them, we have 160 million people. If we have food for them, then is it tough to feed another 700,000 to 800,000?"
Describing Bangladeshis as 'kind-hearted', Hasina said the government has taken measures to provide refugees with food, shelter and healthcare.
“But Myanmar has to take back their citizens.”