(Reuters) - A Kansas law aimed at meeting a state constitutional requirement to adequately fund public schools ran into skepticism from some state supreme court justices on Tuesday.

The high court unanimously ruled in March that Kansas' school funding system fell short of the adequacy requirement, but gave the state until June 30 to come up with a remedy.

Legislation for a two-year funding boost totaling $293 million by fiscal 2019 was enacted by Republican Governor Sam Brownback last month. The law was characterized as inadequate by lawyers representing school districts that sued the state.

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In arguments before the court on Tuesday, justices raised concerns that the new law continued to fall short.

Chief Justice Lawton Nuss questioned why lawmakers pushed aside a recommendation by the Kansas State Board of Education for a $893 million increase. "Aren't they the experts on education?" Nuss asked.

Other justices raised concerns that the state's budget troubles may have put a cap on extra money for schools and that it could take years to determine the outcomes of the new funding formula on student achievement.

Before deciding on a school funding fix, the legislature last month hiked income tax rates over Brownback's veto to address big budget gaps.

Jeffrey King, a special assistant attorney general, told the court the amount of available revenue was "absolutely" a factor for the legislature, but only to ensure the law could meet its additional funding target.

"There is new funding in this formula students will benefit from on day one," King said.

Alan Rupe, an attorney for school districts, said the legislature chose to ignore the state board of education's recommendation and opted for a lower amount that "is not enough."

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"We believe the magnitude of the solution needs to meet the magnitude of the problem," he told the court.

Nuss gave no indication of when the court would issue a ruling.

The lawsuit, which dates back to 2010, also resulted in a state supreme court ruling requiring Kansas to address funding disparities between rich and poor school districts.