TOPEKA, Kan. (AP) — The Kansas Supreme Court signed off Tuesday on a new state law increasing aid to poor school districts, formally ending a threat that the state's public schools could be shut down.

But the court's brief order resolves only a small part of a lawsuit filed in 2010 by four school districts. The court will consider next whether the state is spending enough money overall on its schools, and it could rule on that issue by early next year.

The court issued its three-page order , signed by Chief Justice Lawton Nuss, only a day after Republican Gov. Sam Brownback signed the education funding measure into law. The measure boosts aid to poor districts by $38 million for 2016-17, redistributing some dollars from wealthier districts and diverting funds from other corners of state government because Kansas faces ongoing budget problems.

The GOP-dominated Legislature approved the measure last week in a special session forced by a Supreme Court order last month . The justices said the state's education funding system remained unfair to poor school districts, despite three rounds of changes in the past three years. The court warned that schools might be unable to reopen after Thursday if lawmakers didn't make more revisions.

"We are pleased that Kansas schools will remain open," said Brownback spokeswoman Eileen Hawley.

The lawsuit was filed by the Dodge City, Hutchinson, Wichita and Kansas City, Kansas, school districts. They contend that legislators aren't fulfilling their duty under the state constitution to finance a suitable education for all children, whether they live in rich or poor areas.

The first part of the dispute before the Supreme Court narrowed to an amount of spending equal to less than 1 percent of the more than $4 billion a year the state spends on aid to its 286 school districts. Most of the new aid for poor districts will push down their property taxes levies for schools under a funding system that aims to prevent too much reliance on local taxes so that educational offerings across the state don't vary too widely.

The court said that with the latest changes, legislators have "currently satisfied" its orders and, "Therefore, no judicial remedy is necessary at this time."

"It's on to the next chapter," said John Robb, an attorney representing the four districts.

The court did not say when it will schedule arguments on the second — and larger part — of the case. A lower-court panel ruled last year that the state must increase its annual aid by at least $548 million.

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