Gov. Andrew Cuomo deserves the blame for the MTA’s failing subway service, according to a new poll, as he and Mayor Bill de Blasio fight over funding its improvements.

Roughly 70 percent of New York City voters believe their subway service is either “not so good” or “poor,” according to a Quinnipiac poll released Thursday afternoon. And of those frustrated riders, 40 percent blame Cuomo for the woes of the MTA, a state agency that the governor effectively controls, compared to 21 percent for de Blasio and 20 percent for both leaders.

“These numbers are not good for Cuomo,” said Maurice Carroll, assistant director of the Quinnipiac University Poll. “He certainly wants to be president — he’s certainly got it in his mind, anyway. … He’s going to have to get the subways straightened out, because this is going to escalate.”

The poll comes in the middle of a bitter battle over state and city responsibility for the subway system, which has seen a roughly 200 percent increase in delays over the past five years and a series of high profile service failures in recent months — including two derailments and impactful rush hour outages.

MTA chairman Joe Lhota on Tuesday unveiled an $800 million subway improvement plan, asking for the city and state to split the cost. While Cuomo has made his contribution available, de Blasio has insisted he wouldn’t provide additional funding until the agency spends its money more wisely. He’s criticized Cuomo for diverting more than $400 million in operating funds intended for the agency since 2011 — an action denied by the MTA and Cuomo.

In turn, the governor and Lhota have attempted to put more blame on the city for the system, initially pointing to the 1953 lease agreement that outlines the city owns the subway system’s underlying infrastructure, even though the MTA operates the service.

“I think that’s what [is] really running the day here, that this became a physical crisis that millions of New Yorkers are experiencing and it’s forced, finally, an honest discussion of accountability and the fact that the state runs the MTA,” de Blasio said during an appearance on Hot 97 Wednesday.

After being criticized for his general avoidance of mass transit, the mayor has recently taken to the subways, holding news conferences on platforms and in moving trains to reinforce his point — and the tactic appears to be working, according to Carroll.

“All he’s got to do is keep riding the subway,” Carroll said. “De Blasio has done a good job of focusing on the governor. Is Cuomo in trouble [overall]? No.”

Cuomo’s approval has dipped this summer, with a recent Quinnipiac poll tying the drop to subway performance. But 60 percent of city voters approve of the governor’s job, while 34 percent disapprove, according to Thursday’s poll, which surveyed 877 city voters from July 20 to July 26, with a margin of error of plus or minus 4.1 percentage points.

On Thursday, Cuomo and Lhota again pressed the city to contribute half of the funding for the MTA’s plan.

“The governor this morning also committed to putting up half,” Lhota said during an appearance on WNYC, “and we’re looking for the city to be a partner in doing that.”