NEW YORK—Former American International Group Inc. Chairman and CEO Maurice R. Greenberg testified last week about a sham 2001 reinsurance deal between AIG and General Re Corp., moving a 2005 civil fraud lawsuit against him closer to trial, legal experts say.

The suit, brought by then-New York Attorney General Eliot Spitzer, accused Mr. Greenberg and former AIG Chief Financial Officer Howard Smith of using the deal to hide losses and inflate reserves at the insurer.

In 2008, federal prosecutors obtained five convictions of former Gen Re and AIG executives, including former General Re CEO Ronald Ferguson. Prosecutors said the bogus deal boosted AIG's loss reserves by $500 million without transferring any risk.

During the trial, prosecutors said Mr. Greenberg was an unindicted co-conspirator.

Because of the “threat of prosecution,” Mr. Greenberg previously exercised “limited use” of the Fifth Amendment in asserting his constitutional right against self-incrimination by refusing to testify in the state fraud suit, according to court documents.

However, in a March 2 affidavit filed in New York State Supreme Court, attorneys for Mr. Greenberg said they are “confident” he no longer faces criminal prosecution because the statute of limitations expired Feb. 21. As a result, Mr. Greenberg said he looked forward to testifying during a deposition about the matter, which was ordered by Justice Charles Ramos.

Mr. Greenberg testified last week during a deposition by the attorney general's office. Details of that testimony were not revealed.

Messrs. Greenberg and Smith, who both left AIG in 2005 amid investigations into AIG's accounting practices, repeatedly have denied wrongdoing in the deal. Last September, Mr. Greenberg sought a summary judgment to dismiss the case and accused Mr. Spitzer of bringing the suit to promote his political career. In January, Mr. Smith's attorneys filed a similar motion, said Vincent Sama, a partner with Winston & Strawn L.L.P. in New York and Mr. Smith's attorney.

While Mr. Spitzer dropped portions of the suit in 2006, attorneys for Mr. Greenberg argue in the affidavit that the remaining allegations are “unfounded.”

“Mr. Greenberg looks forward to finally testifying in this case. For five years, he has maintained that he did nothing wrong and that he would be fully vindicated once all the facts came out. We believe that that position has been largely borne out,” Lee Wolosky, a partner at Boies, Schiller & Flexner L.L.P. in New York and one of Mr. Greenberg's attorneys, said in a statement last week. “Mr. Greenberg looks forward to moving forward this final case, most of which has already been dismissed, and which now involves three transactions, none of which had a material impact on AIG's financial position.”

The civil fraud case, which still is in the discovery phase, may move forward this week, legal experts say. At a hearing Tuesday, attorneys for Messrs. Greenberg and Smith will argue their previously filed motions for summary judgment.

While it's possible the judge could make a determination without a full trial, legal experts say it's unlikely because Mr. Greenberg's testimony would likely provide the “factual dispute” required to send the case to trial.

Legal experts also said they would not expect the state to drop the case prior to learning the judge's opinion on summary judgment.

“This does make the attorney general's case harder now,” said Peter Henning, a professor at Wayne State University Law School in Detroit. In civil suits, a defendant who takes the Fifth Amendment may cause what is known as “adverse inference” in which the court might assume certain facts due to the absence of testimony, he said.

“But now, the state does not have that benefit anymore,” Mr. Henning said. “Mr. Greenberg, through his testimony, will be denying any wrongdoing and the state will have the burden of overcoming those statements through circumstantial evidence. It's not impossible, but it will be difficult for the state to prove this.”

New York Attorney General Andrew Cuomo's office, which is handling the case, did not return calls seeking comment.

A spokesman for AIG declined comment.

“It's unclear exactly what (Mr. Greenberg) will say under oath, but I do think (testifying) is a move to put all of this behind (him),” said Fran Semaya, chair of the insurance regulatory practice of Nelson Levine de Luca & Horst L.L.C. in New York, who is not involved in the case.

However, should the case go to trial, it increases the possibility that the parties could reach a settlement, Mr. Henning said.

In January, Gen Re agreed to pay $92.2 million to settle U.S. Securities and Exchange Commission charges that it entered into a fraudulent reinsurance deal with AIG and Prudential Financial Inc.

In 2006, AIG agreed to pay $1.64 billion to settle fraud charges related to its practices with state and federal authorities.

Last August, Mr. Greenberg agreed to pay $15 million to settle civil charges brought by the U.S. Securities and Exchange Commission related to alleged improper accounting transactions that inflated AIG's financial results. Mr. Smith agreed to pay $1.5 million. The duo agreed to the settlements without admitting or denying guilt.