In a major policy setback for Governor Spitzer, the Bush administration is likely to reject New York’s plan to extend health insurance coverage to children of families with income significantly above the poverty level.

Amid a health care clash between the White House and Congress, the Bush administration said it will force New York and other states seeking to expand income eligibility for the State Children’s Health Insurance Program to comply with stricter requirements designed to ensure that wider public coverage does not supplant private coverage.

Spitzer administration officials say they cannot meet the new federal demands — at least for the next several years — and are now facing the strong possibility that the federal government will reject their request for a waiver.

In April, state lawmakers in Albany agreed to increase the income eligibility for the program, which uses federal and state funds to provide health care to children whose families earn too much money to qualify for Medicaid. The income cutoff was raised to four times the federal poverty level, or $82,600 for a family of four, the highest level in the nation for such a program.

Mr. Spitzer hailed the expansion as a major victory for his long-term goal of universal health care coverage, a rare bright spot for the rookie executive in a budget deal full of tough compromises.

In a letter sent Friday to state health officials around the nation, the director of the Department of Health and Human Services’s Center for Medicaid and State Operations, Dennis Smith, outlined several conditions under which states, such as New York, would be allowed to extend coverage to children in families with income levels of more than 250% of the federal poverty level.

Most troublesome for New York and other states is the prerequisite that states enroll at least 95% of children who are below 200% of the poverty level and eligible for Medicaid or Schip.

New York falls short of that mark by 5 to 10 percentage points, according to the state’s Medicaid director, Deborah Bachrach.

“This is tremendously problematic for New York,” Ms. Bachrach said. “There is no state in this country that has reached 95%. The effect of this letter is to prevent states from expanding their coverage.”

The federal policies also limit eligibility expansion in other significant ways. Under New York’s proposal, children could start receiving government-subsidized health care if they have been uninsured for as little as six consecutive months. Children under the age of 5 or those whose parents are out of work could switch immediately to state coverage.

Aiming to prevent the “crowding out” of private coverage, the Bush administration is now requiring a minimum one-year waiting period — with no exceptions.

Mr. Spitzer has set a goal of covering the estimated 400,000 children in New York who are uninsured.

The overwhelming majority of those children, in fact, were already eligible for state-subsidized health care before the Legislature raised the income threshold. The change extends subsidized health insurance to only about 60,000 children who previously were not eligible.

While the number represents a small percentage of uninsured children, Spitzer officials say the expansion of the child health care program is a crucial component of their effort to encourage more lower-income families to enroll.

The administration’s aim is to covey a message that subsidized insurance isn’t only for poor people, officials say.

If the Bush administration denies New York’s application, New York could appeal the decision. In the meantime, the Spitzer administration is lobbying federal lawmakers to pass a reauthorization of Schip that would prevent the Bush administration from setting stricter guidelines.

Mr. Smith issued the letter a day after two Republican senators, Pat Roberts of Kansas and Charles Grassley of Iowa, called on the Bush administration to reject New York’s application, arguing that Mr. Spitzer’s request to raise the income threshold to 400% conflicted with the original intent of the federal child health insurance program.

The House and Senate earlier this month passed different versions of a plan to reauthorize and expand Schip. While the Senate version has bipartisan support, President Bush has vowed to veto either bill, saying both plans pose a threat to private insurers.

Conservative opponents of the legislation have accused the Senate of seeking to raise income eligibility levels to 400% and have urged Mr. Bush to block the bill.

The letter by Messrs. Grassley and Roberts is essentially an attempt to counter the criticism by drawing attention to the Bush administration’s power to approve or reject proposals from states to extend coverage to higher income residents.

Had the Bush administration approved New York’s plan, Senate Republicans would have attacked Mr. Bush for opposing the Senate bill but permitting New York to lift its income threshold.