Christian Geselle, the mayor of Kassel, confirmed that the governments worked to address “looming financial shortfalls.” But the mayor’s office declined to provide specific figures, saying that accountants are examining the books and a full report is due later this month.

“As shareholders, the city of Kassel and the state of Hesse have agreed that the company’s liquidity must be secured beyond that,” Mr. Geselle said in a statement. “Documenta is inextricably linked with Kassel.”

Just how much the cost of the exhibition escalated and exactly who is at fault remain matters of robust debate. The artistic director of the exhibition, Adam Szymczyk, said in an interview that its economic plan was created before he was appointed, that it had not been sufficiently adapted to take account of the double-venue costs and that his team had been forced to work “under terrible budget constraints.”

“What is happening now is an attempt to make this a problem exhibition because of some financing issues at the end,” Mr. Szymczyk said.

Founded in 1955, the quinquennial “museum of 100 days” transforms working-class Kassel — which brands itself “Documenta City” — into a cosmopolitan hub of creative activity and brings in welcome tourism revenue. Often described as the most important art exhibition in the world, Documenta is seen as a bellwether for the relevance and direction of art internationally. It is conceived as an exhibition that takes risks, and in recent days its organizers have used strong language to suggest that its high-concept ambitions were being leadened by government leaders too focused on the bottom line.