The call from Human Rights Watch came as the UN General Assembly prepared to convene in New York, with the crisis in Myanmar high on the agenda.
It also came on the eve of a highly-anticipated national address on Tuesday by Myanmar's civilian leader Aung San Suu Kyi, her first on the crisis in Rakhine state.
The exodus of Rohingya refugees from mainly Buddhist Myanmar to neighbouring Bangladesh has sparked a humanitarian emergency. Aid groups are struggling to provide relief to a daily stream of new arrivals, more than half of whom are children.
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The number also includes 70,000 pregnant or breastfeeding women, according to Bangladesh's information minister Hasanul Haq.
Myanmar has suggested it will not take back all who had fled across the border, accusing them of links to the Rohingya militants whose raids on police posts in August triggered the army backlash.
Any clear moves to block the refugees' return will likely anger Bangladesh Prime Minister Sheik Hasina. She will use the General Assembly to press Myanmar to take back all the Rohingya massing in shanty towns and camps in Bangladesh near the border.
Human Rights Watch also called for the "safe and voluntary return" of the displaced as it urged governments around the globe to punish Myanmar's army with sanctions for the "ongoing atrocities" against the Rohingya.
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"The United Nations Security Council and concerned countries should impose targeted sanctions and an arms embargo on the Burmese military to end its ethnic cleansing campaign against Rohingya Muslims," the group said in a statement.
Myanmar's military was hit with Western sanctions during its 50-year rule of the country. But most have been lifted in recent years as the generals have allowed a partial transition to democracy.
"Burma's senior military commanders are more likely to heed the calls of the international community if they are suffering real economic consequences," said John Sifton, HRW's Asia advocacy director.
Nobel peace laureate Suu Kyi has shocked the international community with her near-silence on the plight of the Rohingya and her failure to condemn the actions of the army, with whom she has a delicate power-sharing arrangement.
Speaking to the BBC over the weekend, UN Secretary General Antonio Guterres said Suu Kyi had a "last chance" to stop the humanitarian calamity.
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