And administrators in some parts of the country - including rebel controlled areas in Kachin and Wa states - said they were barring census takers because they worry the count will be used for political purposes.
Myanmar only recently emerged from a half-century of military rule and self-imposed isolation. No one knows how many people live in the predominantly Buddhist nation. The most accepted estimated, around 60 million, is based on extrapolations from the last count in 1983, that experts say was hugely flawed, leaving out many religious and ethnic minorities.
The enumerators - most of them school teachers wearing white blouses, green traditional lounge and khaki-colored waistcoats - started going door-to-door at 7am (7.30am Thai time) Sunday.
They hope to reach 12 million households by the time they finish their job on April 10.
Their long, complicated questionnaire - a collaboration between the government and the United Nations Population Fund - seeks information that goes well beyond the number of people living in each home, from literacy rates, employment levels and disabilities to access to clean water and fertility rates.
But it also includes sensitive, and highly controversial, questions about race and ethnicity that human rights groups have repeatedly warned could put vulnerable populations at risk.
They are especially worried about Rohingya Muslims in the western state of Rakhine, who have been the targets of Buddhist mob attack in the last two years that have left more than 200 people dead and sent another 140,000 fleeing their homes.
The government considers members of the religious minority to be Bengali immigrants, though many arrived generations ago, and denies them citizenship by national law.
Worried the census would legitimise the status of Muslims, Buddhists in the state have vowed to boycott it. With tensions soaring, they attacked the homes and offices of foreign aid workers last week, forcing the evacuation of almost all staff.
On Saturday, Ye Htut, the presidential spokesman, announced that Rohingya would not be allowed to identify themselves as such on the ballot.
''It will be acceptable if they write `Bengali' . we won't accept them as `Rohingya,''' he said after meeting with President Thein Sein and political parties.
The United Nations gave repeated assurances that the Rohingya would be allowed to identify themselves by that name. The British embassy protested the government's decision.
''The government has committed to run the census in line with international standards, including allowing all respondents the option to self-identify their ethnicity,'' it said in a statement.
Ethnic minorities, which together make up about 40% of Myanmar's population, have also expressed concern about the process. They argue they were not properly consulted ahead of the census, which requires respondents to identify themselves as one of 135 ethnic groups. Long suspicious of the government, they worry the classification system could be used for political gain.
In some cases, the ethnic groups listed on the survey are split up in too many subdivisions.
The Chin, for instance, account for 53 of the categories, though many of the names listed are simply of villages or clans, not separate ethnic groups, fracturing the already small group. In other cases, subtribes with different ethnicities are grouped together, increasing the chances of misrepresentation.
An ethnic group calling itself Tai Nai or Red Shan, which lives in the Sagaing region and the states of Shan and Kachin, complained that they were not included among the 33 subtribes of the Shan.
Khaing Khaing Soe, director of the department of population, was undeterred by rebel threats to deny access to census workers.
''We will go to every corner of the country and will conduct the census according to international standards,'' she told The Associated Press. ''We will not exclude any area.''
She also said anyone who tries to stand in the way of enumerators will be punished.