That drew an immediate rebuke from McGreevey lawyer Steve Haller, who said, "we will appeal or not appeal at our own discretion."
A private meeting with the judge in the case is scheduled for Monday.
Matos has claimed that McGreevey, who resigned from office in 2004 after declaring himself "a gay American," duped her into marriage because he needed the cover of a heterosexual relationship to advance his political career.
Union County Superior Court Judge Karen Cassidy granted the McGreeveys' divorce last month, denying her alimony but ruling that she is entitled to a portion of their joint assets totaling $109,000.
The judge did not rule on the fraud claim, which was filed separately. However, she did determine that Matos was not entitled to recoup money because her time in the governor's mansion was cut short by her husband's abrupt resignation.
Steven J. Eisman, a lawyer who specializes in family law in New York, said fraud claims are usually used by people seeking annulments and those trying to set aside pre- or post-nuptial agreements.
He said Matos would have an uphill climb pursuing fraud against a gay man, and she would have an even tougher time winning damages.
"The only thing it might give her is a paper judgment," he said. "It's a threat without backing."
"Dina wants an end to the litigation between these parties," Post said. "If Jim abides by the judge's ruling, it will be over with."
The McGreeveys' bitter parting was evidenced during a messy four-week divorce trial in which she portrayed him as purposefully underemployed to avoid paying alimony and he portrayed her as a connoisseur of high-end clothing and other material things that were well beyond her means.
The McGreeveys' marriage publicly unraveled when he acknowledged an affair with a male staffer, although the staffer denied the affair and said he was sexually harassed by the governor. The McGreeveys officially split when they moved out of the governor's mansion and into separate homes.
The divorce trial was held this spring after the couple failed to come to terms on alimony, child support and other financial matters. They agreed to share custody of their daughter.
In her written ruling, Cassidy lamented the animosity she witnessed during the couple's divorce trial, saying the McGreeveys were blinded by their anger toward one another.
