With the start of the United States Open tennis tournament just days away, New York City’s comptroller accused the tournament’s organizers of underreporting at least $31 million in revenue over the past four years and said the city was owed $311,000 in back rent for use of the Open site in Queens.

The comptroller, Scott M. Stringer, said the United States Tennis Association, which operates the lucrative tournament and leases the grounds of the U.S.T.A. Billie Jean King National Tennis Center from the city, had obstructed an audit by his office, and he and other elected officials called for a renegotiation of the lease agreement that has been in place since 1993.

“Whenever the city enters into an agreement with a multimillion private entity, we have to protect New Yorkers first,” Stringer said at a news conference outside the tournament grounds on Thursday. “We can’t allow the city to have a raw deal.”

The U.S.T.A. disagreed with many of the findings of the audit, and Danny Zausner, the chief operating officer of the National Tennis Center, said that about 40 percent of the disputed amount had already been paid to the city. Zausner added that he saw no need to renegotiate the terms of the lease.