ALBANY — The Senate’s Republican majority on Monday set up a contentious end of session by linking its goal of increasing the number of charter schools statewide to continuing mayoral control of New York City schools.

“We pushed for removal of the charter cap,” said Senate Majority Leader John Flanagan (R-East Northport) on Monday. He referred to the failed attempt in April budget negotiations to eliminate the cap that restricts the creation of more charter schools despite growing numbers of students on waiting lists.

The Assembly’s Democratic majority supports a lengthy extension of control of city schools by Democratic Mayor Bill de Blasio, but strongly opposes lifting the charter school cap.

“One of the things the city continues to do is flout the law and make sure the charter schools [face] unbelievable difficulty to secure space,” Flanagan said. “I’d rather stop playing around.”

Charter schools are publicly funded, but privately operated, public schools that compete with traditional schools for students and per-pupil funding. The state’s teachers union, influential in the Assembly and major campaign contributors, argues that funding for charter schools hurts traditional public schools.

“I think mayoral control should be extended on its own merits,” said Assembly Speaker Carl Heastie (D-Bronx). “We’re not interested in adding any other criteria to extend the governance of schools.”

Although Senate Republicans strongly supported mayoral control under Mayor Michael Bloomberg, a close political ally and benefactor, the Senate majority has been less inclined to provide anything but 12-month extensions to de Blasio.

The liberal mayor has worked to elect a Democratic majority in the chamber.

Such collisions at the end of the session are often a catalyst to create bigger deals of disparate issues using the pressure of the deadline and the political need to show results for the year’s work. The session is scheduled to conclude June 21.

Gov. Andrew M. Cuomo, a Democrat, has supported expansion of charter schools, which is pushed by major campaign contributors to Senate Republicans and the governor.