RALEIGH — North Carolina Republicans offered wide-ranging legislation Thursday that fixes anticipated class-size challenges in the public schools next fall, but includes other provisions that give Gov. Roy Cooper and other Democrats heartburn.

A bill negotiated by House and Senate GOP leaders and unveiled at a news conference would require classes in kindergarten through third grade to phase in lower teacher-student averages and maximums by the 2021-22 school year.

The current law would have required the limits take effect next school year, but school districts said meeting them now would have forced the elimination of music, arts and physical education teachers, or required higher class sizes in other grades.

Parents and teacher groups, along with Cooper, urged a fix, and Republican lawmakers said they found one that also located dedicated funds for these “program enhancement” teachers, starting with $61.4 million statewide next fall and growing over time.

“I believe that we have arrived at a data-driven solution that will achieve the smaller classes that we all support and the taxpayers have paid for,” said Sen. Chad Barefoot of Wake County, who helped negotiate the class-size agreement. “We’ve done it with a time frame and a timeline that will allow our schools to be able to implement it successfully.”

The measure, which still would need full House and Senate approval, also would direct funding for the state’s pre-kindergarten program to grow by another $19 million by mid-2021 so that all children who qualify for preschool could receive it.

But the measure also would divert $57 million from utility companies wanting to build the Atlantic Coast Pipeline to public schools, instead of using it for environmental and economic projects as Cooper’s office worked out in a memorandum of understanding with utilities seeking to build it.

Republican lawmakers have questioned the deal and Cooper’s actions, saying the General Assembly decides how money coming to the state should be spent. Half of the money would be directed to schools in eight eastern North Carolina counties where the pipeline runs through.

“This legislature is not governed by the terms of the (memorandum),” GOP Sen. Paul Newton of Concord said.

The proposal also would rework a combined ethics and elections board that the state Supreme Court struck down last month. A majority of the justices had ruled that the law approved last spring had prevented Cooper from carrying out his policies because it forced him to fill half the eight-member board with appointees offered by the state Republican Party.

A new board model would create a new ninth member who would have to be someone registered neither as a Democrat nor a Republican, and give Cooper the ability to remove any member as he chooses. Rep. David Lewis of Harnett County, the House Rules Committee chairman, said the changes would comply with the majority opinion, which still has yet to be reviewed by a lower court.

The reaction by Cooper’s office was mixed.

“It’s clear that the legislature finally bowed to public pressure on class size and expanding pre-K, which is positive for our students, but it’s unfortunate that it has been lumped in with political shenanigans,” Cooper communications director Sadie Weiner said in a release.

Republicans have large enough majorities in the House and Senate to override any Cooper veto.

“We encourage him to either sign the bill, because I don’t think he can object to the policies that are in the bill, or let the bill become law,” Lewis said. The House won’t vote for the full measure, which by legislative rules can’t be amended, until early next week. The Senate could vote as early as Friday.

House Minority Leader Darren Jackson of Wake County said the disparate topics in the bill are designed to put Democrats in a political predicament in an election year.

“We’re going to have to talk some about it,” Jackson said. “There will be a lot of support obviously for the class size and pre-K fix.” The rest of the bill, he said, “is an attempt to get the governor to veto it or us to vote against it so they can run political ads.”