Just weeks after an appeals court said the Legislature, not a judge, had to make state budget decisions, advocates of increased spending on New York City schools are renewing their legal efforts.

The budget approved last week by the governor and Legislature increased operating funds for the city’s schools by $400 million and fully funded $9.2 billion in capital spending for things like building schools.

The plaintiffs, the Campaign for Fiscal Equity, a coalition of parents and community groups, are asking for at least $4.7 billion a year in additional operating spending for the city’s schools. The Campaign has been waging a 13-year legal battle in which courts have ordered additional spending. The orders have not been fully complied with by the Legislature and the governor, who has been fighting the spending orders in court.

The Campaign for Fiscal Equity filed a request with the state’s highest court yesterday, asking it to force Albany lawmakers to follow a lower court’s order to increase spending for city schools.

At the heart of the appeal filed yesterday is the question of whether the court has the power to order lawmakers to make budget decisions.

Last month, the appellate division of the state Supreme Court ruled that city schools were being shortchanged by at least $4.7 billion. But in its 3-2 ruling the court said it was up to state lawmakers, not the judicial branch, to decide how much money was needed to provide the city’s 1.1 million schoolchildren with a sound education.

“There’s no doubt that the court has the power to enforce this if it chooses to do so,” an attorney for the Campaign for Fiscal Equity, Michael Rebell, said.

The latest development in the lawsuit has raised red flags among some legal experts.

“You’re potentially provoking a constitutional crisis,” the director of the center for legal policy at the Manhattan Institute, James Copland, said yesterday. “Are we going to have an elected Legislature making the taxing and spending decisions for us – individuals that we can throw out of office – or are we going to have unelected people making those taxing and spending decisions?”

A professor of law at New York University, David Schoenbrod, said a decision in this case in favor of the plaintiff would be unprecedented in New York courts.

“What the court can do is to declare that the current situation is unconstitutional, but the enforcement would have to come through the political process, which is not chopped liver considering that education is an issue that grabs the attention of a great majority of New York State voters,” Mr. Schoenbrod said.

The Campaign for Fiscal Equity is asking the Court of Appeals to hear oral arguments within 30 days and issue a ruling in June before the end of this legislative session. Both the Campaign for Fiscal Equity and the governor declared victory last month when the appellate division issued its ruling.

A spokesman for Mr. Pataki said yesterday that he was “surprised” by the appeal. The state’s lawyers are reviewing the court papers and will decide if they are going to file a cross-appeal.