New York Seeks to Press Trial of A.I.G.'s Ex-Chief To pursue its civil fraud case against the American International Group's former chief executive, Maurice R. Greenberg, the New York attorney general's office is taking an unusual step. It is giving up the right to contest Mr. Greenberg's $115 million settlement of a separate class-action lawsuit - and the right to win up to $6 billion worth of cash damages in its own legal action - to help expedite a trial that would put the former A.I.G. executive on the stand. In a letter to a state court judge sent on Thursday, the office of the attorney general, Eric T. Schneiderman, wrote that it would continue to seek punishments against Mr. Greenberg, including a ban from the securities industry and a ban on serving as a director or officer of a publicly traded company. While applauding Mr. Schneiderman's decision to drop claims of cash damages, a lawyer for Mr. Greenberg criticized the effort to bring the case to trial. "Mr. Greenberg, in his role as "control person" at A.I.G., has already voluntarily stipulated with the S.E.C. to broader injunctive relief than the New York attorney general could obtain in any event," the lawyer, David Boies, said in a statement. This case is over. Someone should put it out of its misery. The move is meant to finally bring the eight-year-old case against Mr. Greenberg and a former A.I.G. chief financial officer, Howard Smith, to trial. The legal battle, rooted in accusations that the insurer committed accounting fraud that led to a $3.9 billion restatement in 2005, has been carried out by Mr. Schneiderman and two of his predecessors: Eliot L. Spitzer and Andrew Cuomo. The actions by A.I.G. at issue in the two cases predate the insurer's $182 billion taxpayer-financed bailout in the fall of 2008. But Mr. Schneiderman's case faced a blow this month when Mr. Greenberg and other defendants agreed to pay $115 million to settle the class-action lawsuit filed by A.I.G. investors. The federal court judge overseeing that suit approved the settlement on April 10, describing it as fair. Other defendants had already settled the investor lawsuits; A.I.G. itself paid about $725 million last year. The attorney general asserted in a court filing late last year that a settlement of the class-action lawsuit would still allow him to pursue his case. But lawyers for Mr. Greenberg have contended that the latest settlement effectively wipes out what they contend are duplicative claims that Mr. Schneiderman had been pursuing in his lawsuit. They are pursuing a motion for summary judgment that would dismiss the attorney general's claims, and have argued that a separate settlement with the Securities and Exchange Commission already included injunctive relief. Rather than being tied up in a court fight over pursuing cash damages that Mr. Schneiderman was unlikely to win, he will instead be free to focus on forcing the former A.I.G. chief to testify, according to people briefed on the matter. The attorney general has viewed putting the former A.I.G. chief on the witness stand as more important than securing additional money on top of the class-action lawsuit. "Attorney General Schneiderman feels strongly that individuals in the financial services industry who perpetrate fraud, no matter how wealthy or powerful, must be held publicly accountable," Damien LaVera, a spokesman for Mr. Schneiderman, said in a statement. And that is why we believe justice will best be served by proceeding to a long overdue trial of Mr. Greenberg as quickly as possible.