TOPEKA, Kan. — Top Kansas Republican lawmakers moved Saturday to break their impasse over how much to increase spending on the state’s public schools, feeling growing pressure to pass a plan that would satisfy a court mandate.

The state House approved a bill that would phase in a $534 million increase in education funding over five years.

The 63-to-56 vote sent the measure to the Senate, with GOP leaders planning a vote soon to determine whether the measure goes to Republican Governor Jeff Colyer, who has endorsed it.

Colyer and some members of the GOP-controlled Legislature have worried that a frustrated Kansas Supreme Court would take the unprecedented step of preventing the state from distributing dollars through a flawed education funding system, effectively closing schools statewide.

‘‘I want to be a part of the solution,’’ said Representative Tori Arnberger, a conservative Great Bend Republican. ‘‘It’s time to be problem solvers.’’

Legislators expected a close vote in the Senate. The Senate previously passed a plan to phase in a $274 million funding increase in over five years, and its GOP leaders argued that a significantly larger boost in spending would force lawmakers to raise taxes within two years.

The new plan is close to one already approved by the House, with the same amount of new dollars. though previously the estimate was lower, roughly $520 million.The new plan adds policy initiatives proposed by the Senate in its plan, including funding to allow all high school students to take the ACT college-entrance exam or its vocational equivalent.

Negotiators for the House and the Senate had several rounds of talks on Friday to resolve their differences but made little progress on the core issue of how much spending should increase.

Colyer argued in a statement Saturday that the new plan could be sustained without increasing taxes.

‘‘The time to act is now,’’ Colyer said. ‘‘Kansas students, teachers, and families need to know their schools will remain open and be funded adequately and equitably.’’

The Kansas Supreme Court declared in October that the state’s current funding of more than $4 billion a year is insufficient for lawmakers to fulfill their duty under the state constitution to finance a suitable education for every child.

The high court gave Republican Attorney General Derek Schmidt until April 30 to report on how the Legislature responded. Schmidt sent a letter Friday to legislative leaders in both parties, expressing ‘‘profound concern’’ that no school funding bill had passed.

The latest proposal drew criticism on both the left and right.

Democrats argued that it would not increase spending enough to satisfy the court. The justices did not provide a specific funding target but hinted that it could be $650 million more a year.

‘‘We are getting graded at the end of it,’’ said Democratic Representative Brandon Whipple of Wichita. ‘‘You are still getting an F.’’

But conservative Republicans said the court is improperly encroaching on the Legislature’s power to determine the state budget and that a big increase in spending wouldn’t lead to higher student performance.

Conservative GOP Representative Randy Garber of Sabetha argued that problems with public education stem from US Supreme Court decisions in the early 1960s declaring school-sponsored prayer and Bible reading as unconstitutional.

‘‘If we don’t fix society, we won’t fix our schools,’’ Garber said in concluding a 13-minute speech. ‘‘I say the way to fix our schools is to put prayer and the Bible back and give it a chance.’’

In Oklahoma, teachers were planning their second week of protests over state education funding.

The state Legislature on Friday approved an additional $40 million for public schools, but the head of the Oklahoma Education Association, the state’s largest teachers union, said it was not enough.

Two bills approved by the state Senate — one taxing certain internet sales and another expanding tribal gambling — were sent to Goveernor Mary Fallin, who will decide whether to sign the revenue-raising measures into law.

Alicia Priest, president of the teachers union, said that for the protest to end, lawmakers must eliminate a capital gains tax exemption and the governor must veto a repeal of a proposed lodging tax.

West Virginia teachers won a 5 percent pay increase after striking for nine days last month. That ignited protests in other Republican-led states, including Kentucky and Arizona.