The U.S. Census Bureau said Tuesday that it omitted more than 1.5 million people belonging to ethnic minorities in the 2010 count, though it defended the accuracy of all other figures.

The bureau released estimates of over- and undercounting in the 2010 Census.

The document calculated some 16 million omissions in the 2010 Census, which included people whose information could not be checked because they incorrectly filled out the questionnaires sent them in the mail.

The report said that in total the Census omitted close to 2.1 percent of African-Americans and 1.5 percent of Hispanics, who together add up to some 1.5 million people who were not counted as they should have been. In any case, these percentages were not statistically different from the results of the 2000 Census, the bureau said.

The 2010 Census also failed to include 4.9 percent of indigenous people living on reservations.

“We’ll use these coverage estimates to build a better 2020 Census,” Census Bureau Director Robert Groves said.

The analysis of problems in the 2010 Census was released at a time when some 100 U.S. cities, including New York, were challenging the official counts, considering them too low.

In general, the erroneous counting occurred less among people who returned their demographic questionnaires in the mail than among those who gave their answers to volunteers doing door-to-door interviews.

The 2010 Census, which cost $15 billion - an unprecedented amount meant in part to encourage the participation of minorities - also unduly added some 36,000 people to the national population, or 0.01 percent of the total.

That error was due, according to the Census Bureau, to counting white citizens twice if they had several homes. The error in the 2000 Census had been 0.05 percent.