New federal Census figures assert that New York City’s population grew by a total of 587 people between 2005 and 2006, a number the Bloomberg administration says substantially underestimates the city’s tremendous growth.

Before the numbers were even public — they were slated for release today — the city vowed to contest the figures, claiming that the methods the Census used aren’t the best way to get an accurate count in a city as dynamic as New York.

At stake are tens of millions of dollars in federal and state funding each year, as population in part determines the apportionment of aid for various programs. After the city successfully contested the 2005 figures last October, adding 70,000 to the initial estimate, Mayor Bloomberg said in a statement that an additional $23.1 million for affordable housing would come to the city.

Challenging the Census’s estimates has become something of an annual tradition for the Bloomberg administration, as this will mark the fourth year straight the city has contested the federal numbers as failing to capture thousands of New Yorkers. The Census Bureau put the city’s population in mid-2006 at 8.21 million, up 2.6% from 2000.

Late last year, the city released a report projecting that its population would grow by more than 1 million by 2030, bringing the city’s total population to 9.1 million, with an increase of nearly 400,000 people expected between 2000 and 2010.

Mr. Bloomberg routinely cites the figures as justification for various large projects and infrastructure improvements, as the city needs to make room for an extra million people.

The Bloomberg administration says it is certain of its contention that the city is growing. It says the Census’s general method simply doesn’t work for New York.

“Given the comings and goings of people in New York, it’s difficult to quantify accurately with the Census Bureau’s methodology,” a spokeswoman for the New York City Department of Planning, Rachaele Raynoff, said, adding that the challenge to the Census is “collegial.” If one looks at the amount of new residential units being created, it is clear that the city is adding population, she said.

“As long as we have the type of dynamic population that we do, and strong growth that doesn’t get captured, we certainly will challenge it because we want to get our share of resources—that’s very important,” Ms. Raynoff said. The city has been granting permits for tens of thousands of new housing units each year, and few of the new buildings appear to be standing vacant.

The move to challenge the Census figures is relatively uncommon throughout the country — only 47 cities, towns or counties were listed on the Census Bureau’s Web site as contesting their 2005 figures. Most of the challenges were successful.

“These people aren’t doing it because of the statistical nicety of it, they’re doing it because money is involved,” a demographer at the Brookings Institution, William Frey, said.

In developing its estimates, the Census Bureau tracks births and deaths, along with migration, which can be difficult to measure, demographic experts say. Because New York has a higher proportion of immigrants and young, transient individuals than many parts of the country, a different estimation method is appropriate, a Cornell professor who works with the city on its estimates, Warren Brown, said.

“For certain counties of population, their standard procedure does not work well,” Mr. Brown said of the Census Bureau. “Based on the indicators and the data that we have, we expect that the numbers will be revised substantially.”

The revised figures are based on data of new residential units. The city has seen a substantial increase in residential building permits issued most every year since 2000. The Census accepts this as an alternative methodology, and barring incomplete data, revises its estimates to match the housing data.

A Census Bureau demographer, Gregory Harper, said neither method was necessarily more accurate.

“It’s hard to say, given the options of an absolute truth, which method is better,” Mr. Harper said. “We’ll find out in 2010.”

Estimates are just that, he added, and they decrease in accuracy as time separates the estimates from the last decennial Census, which the Constitution, in Article I, directs be conducted by “actual enumeration.” Those counts that determine how many members of Congress and how many electoral votes each state has.

When results from the 2000 Census were released, the count showed that estimates for New York City toward the end of the decade were off significantly. In 1999, the Census Bureau estimated that the city had a population of 7.4 million. Just a year later, the 2000 Census showed the New York’s count stood at just over 8 million.