Mayor Bill de Blasio stoked his feud with Gov. Andrew M. Cuomo on Thursday, criticizing him for not acting sooner to break up an alliance between State Senate Republicans and a breakaway group of Democrats that has kept the GOP in control of the chamber.

“This is getting to be a charade,” de Blasio said when asked about a unification deal struck this week between mainline Democrats and the Independent Democratic Conference intended to return Democrats to control of the chamber.

Since December 2012, Senate Republicans and the eight-member IDC have shared control under a power-sharing agreement that liberal Democrats have long criticized.

Cuomo, who will seek re-election to a third term next year, and whose name has been floated as a possible contender for the 2020 presidential race, backed the truce between the two Democratic factions earlier this week. De Blasio said Cuomo should have intervened years earlier.

“It’s very convenient for him now as he’s apparently running for president to be in good graces with the Democratic Party,” de Blasio said. “So now he’s going to move heaven and earth to have a Democratic Senate . . . well he’s been in office since 2011. He could’ve done that from the very beginning, so I’ll believe it when I see it.”

Cuomo Spokesman Rich Azzopardi took a jab at de Blasio’s ambitions, writing on Twitter: “We wish Mayor @BilldeBlasio well on his latest vacation . . . I mean trip to Iowa.” It was a reference to de Blasio’s planned trip to Iowa, whose caucuses officially kick off the presidential race every four years.

De Blasio’s remarks came at an unrelated news conference at City Hall to announce the first wave of changes to his leadership team since he won re-election Nov. 7.

First Deputy Mayor Anthony Shorris and Deputy Mayor for Strategic Policy Initiatives Richard Buery plan to step down early next year, de Blasio said.

Shorris, who served as de Blasio’s second-in-command, will be replaced by Dean Fuleihan, currently the city budget director. Fuleihan will be replaced by Melanie Hartzog, a deputy director at the Office of Management and Budget.

De Blasio has not named a successor to Buery, who played a key role in implementing the city’s free pre- kindergarten program for all 4-year-olds.

The mayor is adding a fifth deputy mayor, Laura Anglin, will serve in the newly created deputy mayor for operations post. Anglin, a deputy state comptroller from 2003 to 2006, joined the administration in January as chief administrative officer.

Emma Wolfe, who served as the mayor’s intergovernmental affairs director has been promoted to chief of staff, de Blasio said.

Wolfe, one of de Blasio’s closest allies, was among de Blasio aides investigated by state and federal prosecutors who examined the mayor’s campaign fundraising practices. Prosecutors concluded the probes earlier this year without pressing charges. But they criticized de Blasio and his aides, saying they violated the “intent and spirit” of state campaign finance laws.

Deputy Mayor for Housing and Economic Development Alicia Glen and Deputy Mayor for Health and Human Services Herminia Palacios will remain in their posts, de Blasio said.