The Spitzer administration is scrambling to correct what lawmakers say is a fatal flaw in a school funding formula that was enshrined into law last year with intention of driving a greater share of state aid into the New York City public school system.

Lawmakers are warning that the new funding system will produce the exact opposite result: Under the existing formula, New York City will receive only 26% of an estimated $1 billion in new state aid, a much smaller slice of the pie than it received in last year’s budget.

A year ago, Governor Spitzer proposed a budget that provided the city with 46% of the additional education dollars.

The difference, which is causing alarm among education groups and forcing the administration to contend with last-minute adjustments to this year’s executive budget, is the result of a glitch in the new funding formula known as “foundation” aid, which formed the basis of Mr. Spitzer’s first education budget.

The funding system was hailed by the governor and education advocates as a simplified and more equitable way of dividing education money among regions. In speeches, Mr. Spitzer has described it as the centerpiece of his public school agenda.

In the past, Albany relied on a jerrybuilt morass of funding formulas that resulted in resources being carved up the same way every year: New York City received about 39% percent of the pot, Long Island 13%, and the rest was distributed to upstate areas.

Education activists, whose court battle against the state stretched the entire Pataki administration, contended the financing system punished districts, particularly New York City, with higher proportions of poorer students.

Mr. Spitzer’s “foundation” formula guaranteed a minimum of 3% increases to school districts, while steering the most money toward “needier” districts.

“This formula, for the first time, has begun to distribute school funding based on educational — rather than political — need, thus targeting our historic funding increases to the school districts that need it most,” Mr. Spitzer said in a speech in November.

What the administration didn’t anticipate was how sensitive the formula was to changes in resident and property wealth. New York City’s share of education funds shrank in large measure due to the sharp increase in property values and incomes in the city between 2004 and 2005, according to the budget office of Senate Republicans.

The result is a dramatic drop in New York City’s share, a small decline in Long Island’s, and a sharp increase in the rest of the state’s. A spokesman for the Democratic-led Assembly said New York City’s share may be larger than the 26% figure cited by Senate Republicans, but is still significantly smaller than a year ago.

The Spitzer administration is expected to adjust the numbers by tacking on additional money for New York City — a difficult option in a time of a $4.3 billion budget deficit — or by jiggering the formula.

Either way, the change is likely to undermine Mr. Spitzer’s claim that his financing system is an improvement over the method that he claimed was overly politicized.

“They couldn’t make the data fit the political need they wanted,” a spokesman for Senate Republicans, John McArdle, said. “We will make sure New York City gets its fair share. We will fix the governor’s problem for him.”

Last year, after Senate Republicans demanded more money for Long Island school districts, the governor signed a budget that stitched on about $100 million of additional aid that favored districts with high taxes.

In the end, Long Island and New York City were awarded roughly the same share of money that they had received in prior decades. Westchester County lawmakers complained bitterly that their percentage increase was stingy compared to that of other counties.

The governor’s office has indicated that it would block attempts by Long Island lawmakers during this year’s budget negotiation to meddle with the “foundation” formula.

“There is no magic bullet for school aid,” a Democratic assemblyman of Westchester, Richard Brodsky, said. “The notion that you can take politics out of government is no more true about school aid than it is about campaigns, and it’s not necessarily a bad thing.”

Budgets officials for the governor did not return calls for comment.