HARRISBURG — Top Republican lawmakers said Wednesday they will meet a key demand of Gov. Tom Wolf’s to boost public school aid, even if it requires a tax increase, but they continued insisting on an end to the traditional benefit in Pennsylvania’s two big public employee pension systems.

Leaders of the Pennsylvania Legislature’s Republican majorities made the offer during a brief meeting with the Democratic governor in the Capitol. It came amid a 7-week-old budget stalemate that has started to shut down crucial safety-net services around Pennsylvania as Wolf and Republicans trade barbs in public.

The move by Republicans meant they were summarily rejecting Wolf’s week-old counterproposal that would have kept most of the traditional pension benefit intact for hundreds of thousands of future public employees. But it also upped Republicans’ commitment by $300 million to the state’s primary funding account for public schools, meeting the $400 million increase Wolf has sought for a total of $6.1 billion.

“I need them to move into my camp on education and so they’ve done I think a pretty good job there,” Wolf told reporters. “But there are conditions and that’s the things we have to talk about.”

Wednesday’s exchange does not resolve a host of other demands brought to the negotiating table by both sides. No new meetings were scheduled.

The GOP’s offer would require Wolf to agree to a top Republican priority of shifting Pennsylvania’s two big public pension systems to a 401(k)-style plan for state government and public school employees who are hired in the future. Wolf has balked at that, as have Democratic lawmakers, and it is staunchly opposed by public employee labor unions.

“This is a huge move, a huge change in the tenor of the meetings and I would hope that the governor takes this proposal seriously and gets back to us as quickly as possible because this will move conversations quickly to ... be able to finalize a state budget,” Senate President Pro Tempore Joe Scarnati, R-Jefferson, said.

Senate Majority Leader Jake Corman, R-Centre, acknowledged scrounging an additional $300 million would require finding new money. The source of it would have to be negotiated, Corman said.

Republicans contend that switching the pension systems to a 401(k)-style benefit will ensure the state does not roll up another massive debt, such as the projected $50 billion combined debt the systems now face. However, Wolf has said the traditional pension benefit is a more efficient way to ensure retirement security for public workers.

The stalemate began June 30 when Wolf vetoed the Republicans’ $30.2 billion budget package, saying it did not do enough to help public schools still struggling after the GOP’s deep cuts in aid in 2011 and that it worsened the state government’s long-term deficit.