NEW YORK—Former American International Group Inc. Chairman and Chief Executive Officer Maurice R. Greenberg is seeking to dismiss a 2005 lawsuit filed against him and former AIG Chief Financial Officer Howard I. Smith by then-New York Attorney General Eliot Spitzer.

In a memorandum filed Tuesday in the New York Supreme Court that seeks a summary judgment dismissing the case—now led by New York Attorney General Andrew Cuomo—Mr. Greenberg said “virtually all” of the allegations made by Mr. Spitzer in his original complaint have been dismissed.

He said allegations against him involving three remaining matters, including the sham 2001 finite reinsurance deal between AIG and General Re Corp., are unfounded and “miniscule relative to AIG’s size.”

Four former Gen RE executives and one from AIG were convicted in connection with the finite reinsurance deal.

One of the other matters described in the heavily redacted 102-page memorandum involves charges that AIG had improperly used an offshore vehicle, Barbados-based CAPCO Reinsurance Co. Ltd., as a shell corporation to take on auto warranty losses the insurer had generated in the mid-1990s as way to get them off its books.

The third situation involves charges that AIG used a complex arrangement to convert underwriting losses in its Brazilian life insurance business to investment losses in 1999 and 2000.

“In the course of extensive discovery conducted in its case, no witness has testified that Greenberg sought for AIG to enter into improper transactions or that Greenberg had knowledge that any of these transactions were improper,” the memo states.

“At all times Greenberg—who, during relevant periods, ran an enormous global company that operated in 130 countries—relied on legal counsel, on internal accounting experts, on external auditors, on actuaries and on AIG’s counterparties to structure and account for the millions of transactions entered into each year in an appropriate manner.”

The memo states that Mr. Spitzer's “dogged pursuit of a handful of immaterial transactions from a decade ago, in the face of a record that is bereft of any admissible evidence Greenberg was aware of or wrongfully benefited from any improprieties, has been and remains an enormous waste of resources that could have been better employed investigating other matters, including the total collapse of AIG that came about under the new management installed at Spitzer's insistence after Greenberg left.”

The memo also states that Mr. Spitzer had threatened AIG’s board of directors with a corporate criminal indictment unless Mr. Greenberg was removed. It says he was planning to run for New York governor at the time and “has since admitted that this high-profile pursuit of Greenberg achieved its intended objective of enhancing his reputation as he pursued higher office.”

Mr. Spitzer resigned as governor last year following a sex scandal.

An AIG spokesman had no comment. Representatives of Messrs. Spitzer and Cuomo could not be reached.