Hank Greenberg should still face trial over sham transactions he is accused of orchestrating while he was head of American International Group , even though New York has dropped most of its claims against him, a lawyer for the state argued on Tuesday.

"We're looking for a deterrent effect," Barbara Underwood, the state solicitor general, told New York's highest court. She said the state wanted an admission from Greenberg, who headed AIG until March 2005.

Greenberg is accused of misleading shareholders over the financial health of AIG through transactions a decade ago that the attorney general has said were designed to help boost the company's share price.

New York Attorney General Eric Schneiderman dropped claims for as much as $6 billion in damages last month, but he is still trying to have Greenberg, 88, banned from the securities industry and from being a director or officer of a public company.

New York's Court of Appeals heard arguments on Tuesday over whether the case against Greenberg and former Chief Financial Officer Howard Smith should go forward. A decision could come in June.

David Boies, a prominent lawyer who represents Greenberg, asked the judges to throw out the case before trial, arguing there was no evidence of wrongdoing and no basis for injunctive relief such as the bans.

"In order to get injunctive relief, you must show either some danger of continuing violation or some ability to ask for disgorgement and restitution," Boies told the panel.

The judges questioned Boies about evidence against Greenberg and they also pressed Underwood about whether the attorney general was seeking a moral victory.

"We're going to trial on that?" Judge Eugene Pigott asked Underwood after she said the attorney general was seeking bans on the two executives.

Underwood responded that the attorney general may also seek disgorgement of ill-gotten gains. She said the state was entitled to go after "performance-based compensation that was affected by these frauds." She declined to cite a figure.

SPITZER'S CASE

The lawsuit, filed in 2005, was one of the biggest enforcement actions brought by Eliot Spitzer when he was New York attorney general.

The case centers on two transactions in which AIG was accused of misleading its shareholders. One, with General Re Corp, a unit of Warren Buffett's Berkshire Hathaway Inc , raised AIG's loss reserves by $500 million without transferring risk. Another, with Capco Reinsurance Co, hid a $210 million underwriting loss in an auto-warranty program.

In court papers, the state has said Greenberg "initiated, negotiated and approved" the transaction with Gen Re "with knowledge of its fraudulent terms." CFO Howard Smith helped implement the deal and also knew of the sham, the state said.

Judge Robert Smith asked Boies if a jury could decide that Greenberg's subordinates wouldn't do "a crooked deal" without asking him.

Boies noted AIG did thousands of transactions, but Judge Smith retorted that the General Re transaction was a $600 million deal. Vincent Sama, an attorney who argued for CFO Smith, also told the court it could not infer the CFO knew what was going on.

Five former officials of AIG and General Re entered into deferred prosecution agreements in which they agreed that aspects of the transaction were fraudulent. Buffett was not accused of wrongdoing.

Greenberg left New York-based AIG in March 2005 after nearly four decades at the insurer's helm. After his ouster, AIG paid $1.6 billion to settle regulators' claims of improper accounting and other practices. AIG also restated financial results for several years.

Last month, a federal court approved a class action settlement between AIG and shareholders over the same transactions that are at the center of the state's lawsuit, forcing Schneiderman to drop his damages claims against Greenberg and Smith.

Boies had been planning to argue in the appeal that federal law prevents the state attorney general from recovering damages on behalf of private entities. That would have been a major challenge to New York's securities fraud statute, the 1921 Martin Act, which attorneys general have wielded against Wall Street since the early 2000s.

But Boies on Tuesday said Schneiderman's move to withdraw the damages claims against Greenberg had rendered that argument moot.

"I believe that's over with," Boies said when asked whether the question of the Martin Act being pre-empted by federal law was still before the court.

The case is People v. Maurice R. Greenberg, New York State Supreme Court, New York County No. 401720/2005

(Reporting by Karen Freifeld; Editing by Eddie Evans and Chris Gallagher)