April 3, 2014 12:36 p.m. ET

YANGON, Myanmar—Census takers in Myanmar aren't collecting data from anyone identifying themselves as Rohingya Muslim, underscoring deep ethnic tensions clouding the country's first census in three decades and prompting condemnation by a United Nations group.

What Rohingyas should be called in the census being completed this week is a heated issue. Buddhist monks and residents in 13 towns across Rakhine state held protests last month to oppose the use of "Rohingya" in the census, saying it would legitimize the Rohingya people's existence in the country and potentially one day lead to citizenship.

The government doesn't recognize "Rohingya" as one of the 135 ethnic groups under Myanmar's 1982 citizenship act. It says such people—a minority Muslim group in the majority Buddhist country—can identify themselves as "Bengali."

The majority of Myanmar citizens consider the Rohingya illegal foreigners and say they think the term "Bengali" more accurately identifies them as immigrants from neighboring Bangladesh. It's unclear how many Rohingyas are in Myamar, but estimates are a few hundred thousand.

The Rohingyas—who are stateless because they aren't recognized as citizens in Bangladesh either—say they have lived in Myanmar for generations and want to be counted in what they consider their homeland.

"We wanted the enumerators to collect our data, but when we said that we are 'Rohingya,' they left our homes," said Zamzan Ali, a Rohingya man living in Buthidaung township in Rakhine state.

Myint Kyaing, director general of Myanmar's population department under the Ministry of Immigration and Population, said census enumerators wouldn't "accept census data or collect information" of people identifying as "Rohingya."

The United Nations Population Fund—which is spearheading the US$75 million census—said Monday that it was "deeply concerned" about the government's decision, which became clear once census data-collection started on Saturday. The census is an attempt to improve the country's statistical data following decades of isolation under a military junta. Such data are used to make decisions about social programs and funding.

"The government made a commitment to conduct the exercise in accordance with international census standards and human-rights principles," the U.N. group said in a statement, adding that the government "explicitly agreed" to the condition that people would be able to declare their ethnicity.

Tensions between Muslims and Buddhists have led to bloodshed in recent years, leaving more than 150 dead and 140,000 displaced, many of them Rohingya Muslims.

The decision to not count Rohingyas could "heighten tensions in Rakhine state," the U.N.'s population fund said, and "undermine the credibility of the census data."

In a statement Wednesday, Marie Harf, deputy spokeswoman for the U.S. Department of State, urged Myanmar to "take steps to ensure its census is conducted in a manner consistent with international standards."

The International Crisis Group, a Brussels-based nongovernmental organization that works to prevent conflict, earlier warned that the census could inflame tensions in Rakhine state, recommending that the form avoid questions of ethnicity and religion, and focus instead on age, gender and marital status.

Human rights groups, including the U.K. Campaign for Burma and Human Rights Watch, called for donors to Myanmar's census—such as the United Nations and the Department of International Development, the U.K. government's development and aid arm—to withdraw financial support to avoid endorsement of what they see as discriminatory policies against the Rohingya, or for the Myanmar government to postpone the process to avoid inflaming tensions.