States in the Midwest had the highest overcounts, while Texas and California had some of the largest numbers of people missed, along with parts of the mid-Atlantic and rural West. Two other big states, New York and Illinois, had overcounts.
Also released Monday were estimates for counties and towns across the country. It's the bureau's follow-up to its announcement last month that it overcounted the country's population by 1.3 million people in 2000 after originally announcing an undercount of 3 million.
The latest estimates will not affect the government's official population count of 281.4 million in 2000.
Nor will it affect how the government distributes at least $185 billion to the states for social services and programs such as Medicaid, or the redrawing of congressional and local political district boundaries.
Still, census officials say they are releasing the estimates to prove how well it counted U.S. residents in the once-a-decade head count. All but 10 states and the District of Columbia had overcounts.
Conceivably, the new figures could be used by cities, counties and advocates for minorities in lawsuits arguing that blacks, Hispanics and other groups were underrepresented. "But there are still some troubling issues with the data," said associate census director Preston Jay Waite.
How well the Census Bureau counts the population, and what to do about errors that are uncovered, has been a contentious issue. Congressional Democrats and civil rights leaders maintain the bureau has not ensured that minorities are counted fully.
Critics say the bureau should have used a complicated statistical method called sampling to make up for historic undercounts of minorities.
Opponents of that method, mainly Republicans, have said the latest estimates prove that sampling actually inserts more error into a census they contend is one of the most accurate in history.
National findings released in March showed an overcount of whites, Asians, American Indians on reservations and young children, while many blacks and Hispanics were missed.
The Census Bureau estimates it was most off in Minnesota, where it overcounted the state's population of 4.9 million by 1.7 percent. Indiana was overcounted by 1.6 percent.
Nevada and Montana had the largest percentage of people undercounted, at 0.5 percent.
The bureau guesses it came closest in Colorado, where it overcounted the state's population of 4.3 million by 331 people, or 0.01 percent. In New Mexico, it undercounted by 321 people, or 0.02 of the state's 1.8 million residents.
California had the largest numerical undercount. The bureau said it missed more than 44,000 people in a state originally counted at close to 33.9 million. It had the largest numerical overcount in Illinois, double-counting 174,000 of the state's 12.4 million residents.
By Genaro C. Armas