The Supreme Court is the final legal option open to Cameron and Tyler Winklevoss, who allege that Zuckerberg stole their idea for the social networking site.
The 9th US Circuit Court of Appeals declined Winklevosses request to have an 11-judge panel review the original ruling, which a three-judge panel had made in April.
In a statement, the Winkevosses' attorney Jerome Falk said he plans to pursue in the Supreme Court the appeals court's decision that a party who is defrauded into entering a settlement agreement cannot challenge the contract for fraud, and the court's decision that statements made in a confidential mediation cannot be used as proof that a party committed securities fraud.
"Settlements should be based on honest dealing, and courts have wisely refused to enforce
a settlement obtained by fraudulent means," Falk said.
The Winklevosses are planning another legal challenge in Boston, where they plan to ask the court to investigate their claims that Facebook and its lawyers concealed instant messages from them during the litigation.
In a written statement after the 9th US Circuit Court of Appeals decision, Facebook said: "We're pleased with the court's decision."
A three-judge panel had ruled in April that the Winklevoss twins cannot undo the $65 million cash-and-stock settlement they reached with Facebook in 2008.
The agreement gave them $20 million in cash and stock now valued at about $200 million. The Winklevosses say they were misled about the value of the stock when they entered into the agreement with Zuckerberg.
The twins' attorney said Facebook held back information about the estimated value of the California-based social networking site at the time of the settlement.
The panel had said in April that litigation in the case "must come to an end" and had thrown out the bid by the Winklevosses to review the settlement.