“And,” he added, “it was only after the public found out about it that they did the right thing.”

The e-mail messages revealed that after the Yankees made concessions over the size of the suite and the food, the team received an additional 250 parking spaces, as well as the rights to three new billboards along the Major Deegan Expressway and whatever revenue they generate.

The messages contrasted with earlier public statements from Seth W. Pinsky, president of the city’s Economic Development Corporation, that the suite was not a big issue and that the city had received it simply as a matter of course. One message said that the acquisition of a suite in the Mets stadium was “a big issue to the mayor.”

Under the new arrangement with the city, the Yankees will be allowed to keep the parking spaces and use of the billboards, and the city will be guaranteed at least $100,000 for each baseball season, even if no one buys the suite. The deal was formalized last month in a letter from Mr. Pinsky to the Yankees president, Randy Levine, that was made public on Tuesday. A similar arrangement is being negotiated with the Mets, which also gave the city free use of a suite in its new ballpark, Citi Field.

Aspects of the stadium negotiations slowly came to light as state and federal lawmakers began raising questions about the deals.

The letter from Mr. Pinsky to Mr. Levine said that the main motivation for the agreement was the term limits extension approved by the City Council, which could allow Mr. Bloomberg to remain in office “for several seasons.”