WASHINGTON (AP) _ The Bush administration today decided not to correct the 1990 census that overlooked more than 5 million people - a decision that will likely cost big cities and states millions of federal dollars over the next decade.

Commerce Secretary Robert Mosbacher said that to adjust the count would be to ''abandon a 200-year tradition of how we actually count people.'' The government has never jettisoned official census numbers in favor of population estimates in the two centuries that it has been counting Americans.

A federal court had ordered Mosbacher to decide by today whether population estimates were more accurate than the census numbers and should be used instead of the head count.

''Before we take a step of that magnitude, we must be certain it would actually make the census better and the distribution of the population more accurate,'' Mosbacher said. ''After thorough review, I find the evidence inconclusive and unconvincing.

''Therefore I have decided that the 1990 census count should not be changed by statistical adjustment.''

The choice was important because the official census numbers are used to determine where billions of dollars in federal money will go and how many representatives each state sends to Congress.

Several big cities and states have vowed to return to federal court to demand the tally be corrected.

By the Census Bureau's own estimate, the census count of 248.7 million is too low by 5.3 million people. Many of those not counted in 1990 were blacks and Hispanics living in large urban areas.

The alternative to the head count is an estimate that comes from a survey of 165,000 households conducted by the government about the time of the census. It is commonly believed that the head count census missed millions of people whose existence was verified in the survey.

Mosbacher's decision was immediately criticized in the jurisdictions that stood to lose the most.

''It could deprive New York of hundreds of millions of dollars in federal aid as we head into the year 2000,'' said Robert Abrams, New York state's attorney general.

''California will not get its fair share of federal funding or full delegation of elected representatives in Washington,'' said Rep. Norman Y. Mineta, D-Calif. The corrected numbers would have given California an additional seat of Congress.

''I am enraged,'' said Rep. Ronald D. Coleman, D-Texas, where the estimate said more than a half-million people were missed. ''The Republicans have, in effect, told minority voters in the United States 'You don't count.'''

Cleveland's city planner, Michael Andrezejewski, said his city would lose $1.11 million a year in federal funds because of Mosbacher's decision. ''I think it's absolutely crazy that they're not going'' to correct the head count, Andrezejewski said.

New York City in 1988 sued to force the government to correct the census numbers and will press for quick action to reverse Mosbacher's decision.

''We'll go back to court,'' David Goldin, assistant corporation counsel for the city, said before Mosbacher's announcement. ''We'll ask the court to order that the census be corrected.''

The estimate found that about 2 percent of the population was missed in the tally taken in April of 1990.

''We counted about 98 percent of all the people living in the United States, an extraordinary feat'' considering the diversity and mobility of the population, Mosbacher said.

Sen. Herb Kohl, D-Wis., said there was no question the 1990 head count missed people, but trying to use the estimated created too many technical problems.

''We have to work very hard now so that hopefully by the year 2000 we'll have the technical capabilities to adjust the undercount,'' said Kohl, chairman of the Senate subcommittee on the census.

''It's good new for Pennsylvania,'' said Rep. Tom Ridge, R-Pa., a member of the House subcommittee on the census. Pennsylvania would have lost a congressional seat if the census had been corrected. ''An adjusted census would spawn endless litigation seeking to adjust the adjustments.''

The year before the census was taken, 45 federal programs distributed more than $17 billion in aid based directly on the count, congressional auditors said.

The amount of federal money depending on the census, directly and indirectly, totaled about $59 billion in 1989, said Michael Murrray, an economist at Bates College in Lewisville, Maine.

More than 30 governments, organizations and individuals representing big cities and populous states have filed suit in New York to force federal officials to correct the 1990 census.

Other lawsuits, like one filed by Wisconsin, ask the courts to forbid any adjustment of the census numbers. Wisconsin would lose a congressional district if the adjustment was made.

Under a court order in the New York suit, Mosbacher could have corrected the census if the government could prove the population estimates were more accurate than the census count, not just for the nation as a whole but for small cities and even neighborhoods.

The programs funded with use of population figures cut across the range of American life. They provided money to feed, educate and house the poor, build and fix highways, run mass transit systems, control air pollution, and treat alcohol and drug addictions.

Moreover, the census numbers are used to draw political districts for big governments and small, from the U.S. House of Representatives down to state legislatures, city councils and town boards.

The 1990 census not only miscounted Americans, it miscounted them unevenly.

People in inner cities, blacks, Hispanics and southerners were more likely to be overlooked. People in smaller communities, whites, Asian-Americans and midwesterners were less likely to be missed.

Critics of the census argue the numbers should be corrected because of their racial, ethnic and class distortion. They say the estimates are more accurate.

Traditionalists say the Constitution forbids using estimates as the census, no matter how accurate. They say the solution is to improve counting methods in time for the next census in 2000.

Correcting the census numbers would change House representation in four states, transferring one seat apiece from Pennsylvania and Wisconsin to California and Arizona.

Pennsylvania's and Wisconsin's congressional delegations are split almost evenly between Democrats and Republicans. California's delegation is predominantly Democratic, and Arizona's is mainly Republican.

An expert in redistricting and voting rights issues, Allan Lichtman of American University, said a census correction would tend to add people to districts that vote for Democrats.

But whether that would actually increase Democratic power in state legislatures ''depends on who's drawing the lines,'' he said.

State legislatures began drawing new districts as early as January, when the Census Bureau began releasing computer tapes containing detailed population counts.

The Census Bureau prepared new tapes containing the revised numbers for overnight shipment to the states in case of a decision to correct the census.