DETROIT - Detroit could run out of cash in a week if a lawsuit challenging an agreement with the state to fix the city’s finances isn’t dropped, the city’s new chief financial officer said Friday, raising concerns of a full-fledged takeover by the state.

Finance chief Jack Martin offered his assessment a day after the state treasurer’s office told city officials that Detroit is at risk of losing $80 million in revenue sharing because of the lawsuit. He said the city will be broke by June 15.

While the city should be able to make payroll for employees, it will be operating under a deficit, he said.

Mayor Dave Bing, who wants the lawsuit withdrawn, told reporters Friday that the agreement with the state could be violated if the city runs out of money.

“It’s an emergency,’’ Bing said. “It is a crisis and we’ve been in a crisis for a long time. This just ups the ante more than anything else. And I think, from a leadership standpoint, it’s incumbent upon us as leaders to deal with this expeditiously, which means ASAP.’’

Bing planned to meet Friday morning with the City Council to discuss the situation, but that meeting was rescheduled for Monday.

Krystal Crittendon, the city’s corporation counsel, filed a lawsuit last week with the Court of Claims in Lansing asking that the consent agreement be overturned. The suit asserts that the state already owes Detroit $224 million in past revenue sharing and that Michigan law prevents the city and state from entering into a consent agreement if one of them owes the other money.

Snyder has said the state doesn’t owe Detroit any money. The state wants Bing to compel Crittendon to drop the lawsuit.

Bing said in a statement Friday that he has urged Crittendon to withdraw the lawsuit but that the city charter gives her “the independent right to take whatever action she deems reasonable,’’ including judicial action, if she thinks the charter has been violated.

Martin said that at least $35 million of the $80 million has been withdrawn from the city’s escrow account. A bond sale was approved earlier this year by the City Council with just over $80 million in interim financing backed by state revenue sharing due Detroit.

The bond sale is not part of the consent agreement, Treasury spokesman Caleb Buhs said Thursday, but the city’s failure to meet its obligations to the sale could lead to it losing revenue sharing.

Without the millions of dollars from the state, Detroit would find it difficult to meet payroll and other bills. Any further slippage in the city’s already poor financial standing could lead the state to reconsider the effectiveness of the consent agreement.

Bing, the City Council and Governor Rick Snyder approved the agreement in April that would allow the state’s involvement in correcting an accumulated budget deficit of more than $200 million and billions of dollars in structural debt. In return, Snyder agreed not to hand the city’s finances over to an emergency manager.