Myanmar's President Thein Sein signed the population control healthcare bill into law last week, state-controlled media announced on Saturday.
The legislation is backed by the Buddhist ultra-nationalist group the Committee for the Protection of Nationality and Religion, known as Ma Ba Tha.
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The group has stoked anti-Muslim sentiment by saying Muslim communities have high birth rates and will eventually overrun the predominately Buddhist country.
"This law targets one religion, one population, in one area," said Khin Lay, founder of the Yangon-based Triangle Women Support Group, which gives women professional and political training and lobbied against the law.
The government denies discriminating against Muslims. It says new the birth law is aimed at improving maternal health and child welfare.
It was unclear how the new law against giving birth in the three-year period would be enforced.
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The United States has said the legislation, which falls under "Race and Religion Protection Laws", has the potential to exacerbate racial and religious divisions in the country.
Washington and the United Nations have called on Myanmar to address discrimination and violence against ethnic Rohingya Muslims. They say the government's policy toward the Rohingya minority is a root cause of mass migration that has led to the humanitarian crisis unfolding on Southeast Asia's seas.
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Other groups have also expressed concerns that the law could further exacerbate tensions in Rakhine State where violence between Buddhists and Rohingya Muslims broke out in 2012. Most of Myanmar's 1.1 million Rohingya are stateless and live in apartheid-like conditions.
"In the case of Rakhine specifically, it will only create misunderstanding between the two communities," said Nwe Zin Win, head of Yangon-based women's rights group Pyi Gyi Khin.
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