The leaders in the Republican-led Senate and Democratic-controlled Assembly on Monday indicated they would push to change Gov. Andrew Cuomo’s plan to require local governments to develop ways of sharing services and scale back his efforts to expand his office’s powers over the state budget.

“I think that we are generally in agreement that there should be the prerogative of the Legislature over the Senate and Assembly and I think we have a number of disagreements with the executive over allowing too much power to go to his authority over the budget,” Republican Senate Majority Leader John Flanagan said.

Lawmakers met Monday afternoon for the start of the joint budget committee process — a meeting known in Albany as the “mothership” and initially held as a way of enhancing transparency in the opaque state budget process, but also a chance for lawmakers to lay out their public priorities in the talks.

While the Legislature has been loathe to surrender powers over making changes to the budget after its approved to Cuomo, the legislative leaders were also skeptical Cuomo’s consolidation plan would remain intact.

“It wasn’t in our one-house,” Speaker Carl Heastie said. “The governor maintains its one of his priorities. We’ll see what happens, but it’s not something that I’d say, at least in our conference, any of the members were too happy moving forward with that.”

The plan would require local governments to work with county officials to find ways of sharing services and consolidating costs with an effort of finding concrete ways of reducing property taxes. The plan would be considered by voters in a referendum this November.

Cuomo has long sought to consolidate and scale back the size of local governments in New York, which he has blamed for the state’s high property taxes — an assertion budget watchdogs say is more tied to the cost of programs like Medicaid or employee pensions.

At the same time, lawmakers contend Cuomo is dangling aid to municipalities over local governments to force the sharing of services — a claim the governor’s office denies.

“Local governments are just saying that’s not really an appropriate carrot or a stick and frankly they deserve that money and they do a lot of shared services now,” Flanagan said.

But Independent Democratic Conference Leader Jeff Klein suggested there would be a compromise possible on the issue.

“If indeed there’s a way they can do these efficiencies and enjoy the benefit of the local level, I think that’s something we can discuss,” Klein said.