NEW YORK—Former American International Group Inc. chief Maurice R. Greenberg was grilled on the witness stand for seven days over the past two weeks in a dispute over the ownership of a large block of AIG shares controlled by Mr. Greenberg's Starr International Co. Inc.

The outcome of the case, which was brought by AIG and is being heard in U.S. district court in New York, hinges on AIG's ability to prove that the two firms, which were once tied closely, had a trust agreement in place, despite the absence of a legal document, experts say.

The block of shares at issue in the case was used to fund a well-known deferred compensation program for select AIG employees until the program was canceled in 2005.

In sometimes testy exchanges with attorneys representing AIG, Mr. Greenberg, who headed both companies for more than three decades and is the key witness in the case, rejected suggestions that his forced 2005 resignation from AIG was the reason he canceled the program.

U.S. District Judge Jed Rakoff previously ruled that the U.S. government bailout of AIG and the circumstances surrounding Mr. Greenberg "s forced resignation cannot be brought up during the trial.

AIG argues the shares were set aside in a trust to back the executive compensation program and sued SICO, alleging SICO improperly converted, or took, the shares and breached its fiduciary duty. The New York-based insurer is seeking $4.3 billion in damages, representing the sale of millions of AIG shares since Mr. Greenberg left the insurer, and the return of more than 185 million shares that SICO controls. The stock was transferred to SICO as part of a 1970 reorganization of AIG and its affiliates.

New York-based SICO argues that the shares were placed aside for several purposes, including protecting AIG from a takeover bid. SICO presented a trust agreement showing the establishment of Starr Chari-table Trust with the Bank of Bermuda in 1970. At the time, the trust and SICO were based in Bermuda.

In testimony last week, Mr. Greenberg said that AIG's compensation program made “many, many millionaires” among AIG executives, but he maintained the program was “not cast in concrete” and could be amended at any time.

In addition, Mr. Greenberg said terminating the plan was the result of a “mutual agreement” between the parties, but conceded he never spoke with his successors at AIG about canceling the plan.

AIG's attorney, Theodore V. Wells Jr. of Paul, Weiss, Rifkind, Wharton & Garrison L.L.P., attacked Mr. Greenberg's credibility and accused him of making false statements.

“Is it the truth that the reference to a mutual agreement is a false statement?” Mr. Wells asked.

“Not to my knowledge,” Mr. Greenberg replied.

AIG rested its case last week after Richard Beattie, an attorney who represented independent AIG directors in 2005, rejected Mr. Greenberg's assertion that Mr. Beattie had advised Mr. Greenberg to end the compensation program for “reasons of corporate governance.” Mr. Beattie is chairman of Simpson Thacher & Bartlett L.L.P. in New York.

Mr. Greenberg also defended his use of the disputed shares since 2005 and said SICO used the $4.3 billion in proceeds from AIG shares that were sold to “diversify its portfolio” and invest in “a variety of opportunities,” including private equity funds, real estate and health care companies.

“SICO also invested in new insurance companies, some of which compete with AIG, right?” Mr. Wells asked.

“We did, but that was our right,” Mr. Greenberg replied.

In its defense, SICO presented documents last week relating to the 1970 AIG reorganization, including proxy statements and amended articles of incorporation that “do not contain any language related to a trust or obligation by SICO to use any of the shares to benefit AIG employees,” said David Boies of Boies, Schiller & Flexner L.L.P., who represents SICO.

But AIG tried to show there was an oral contract based on numerous videotaped speeches, transcripts and interviews by Mr. Greenberg in which he spoke of using the AIG stock for “the benefit of future generations of AIG employees.”

“We put these shares in a trust and that trust cannot be broken by anybody,” Mr. Greenberg told participants of the SICO plan, as it was called then, in a 1996 speech played for jurors. He added that the trust account is set up “so that no one group of individuals can ever raid it.” In a 2000 speech, Mr. Greenberg said there was enough stock in the trust to provide compensation for “a couple of hundred years.”

When questioned on the stand by Mr. Wells, Mr. Greenberg said he was “exaggerating” about the length of time and said he used the term “trust” loosely.

The videotaped speeches and other transcripts likely will help AIG support its claim and be important in establishing intent, said Fran Semaya, chair of the insurance regulatory group of Nelson Levine de Luca & Horst L.L.C. in New York, who is not involved in the case.

Ms. Semaya, speaking personally and not representing her firm, said “a trust is a fiduciary relationship, and you can have one without a contract.”

While AIG does face a challenge, “there is case law that you can prove a trust exists without legal documents.” But she said “the documents will speak for themselves.”

Other observers say the fact the case has reached trial indicates the judge's view that there are substantial “issues of fact” on both sides.

The court also heard testimony last week from two former outside directors of AIG: Carla Hills, a former U.S. Secretary for Housing and Urban Development who served as a board audit committee member at AIG from 1996 through 2006, and Frank Zarb, a former interim chairman of AIG.

Mr. Zarb testified that AIG and SICO did not enter into a mutual agreement to end the compensation plan. Meanwhile, Ms. Hills testified that a trust did not exist as defined by AIG.

AIG has said it would use the proceeds of any judgment to help repay its federal bailout package.

The trial continues this week.