Mayor Bill de Blasio warned state lawmakers on Monday that the city’s education costs could increase by $1.6 billion over the next decade if the state Legislature does not approve an extension to the mayoral control law that grants him authority over the school system.

De Blasio announced the budget projection at a City Hall rally aimed at shoring up support for the extension, which will expire on July 1 if it is not renewed before the Legislature adjourns on Wednesday.

The measure, first approved in 2002, transferred control of New York City Public Schools from a seven-member Board of Education and 32 community school boards to the mayor’s office, with the goal of reforming a scandal-plagued system.

“It is projected that this will cost $1.6 billion more over the next 10 years because we will have to reconstitute all local school boards, and all the administrative staff, and all the redundancy . . . all the paralysis costs money,” de Blasio said, citing figures compiled by his office.

De Blasio was joined by union leaders and city officials, including Comptroller Scott Stringer, who took aim at state Senate Leader John Flanagan (R-East Northport) for delaying an extension vote. Flanagan contends the measure should include a provision for more charter schools in the city.

“What I find outrageous today is that the Republicans in Albany — John Flanagan and his crew — want to get their grubby hands on our kids . . . we’re not going to let them do it,” Stringer said.

Senate GOP spokesman Scott Reif in a statement called Stringer’s remarks “cheap political attacks” and said “we are going to stay focused on extending mayoral control and increasing opportunities so every child can receive a first-class education.”

In Albany, legislative leaders emerged from their first face-to-face meeting with Gov. Andrew M. Cuomo late Monday afternoon saying they were still aiming for an agreement on mayoral control and issues tied to it by Wednesday.

“I still think we have time to reach agreement and, yes, we are leaving on Wednesday,” Flanagan told reporters after a 45-minute closed-door discussion in Cuomo’s office.

Assembly Speaker Carl Heastie (D-Bronx) said no specifics were discussed and no length of an extension for mayoral control is settled.

“We talked about many things and mayoral control, of course,” said Sen. Jeff Klein (D-Bronx), leader of the Independent Democratic Conference that shares power with Republicans in the chamber.

“It was an open discussion,” Klein said.

Flanagan said he would speak to de Blasio Monday night by telephone.

Cuomo would not comment.

With Michael Gormley and Yancey Roy