SAN FRANCISCO — A federal appeals court has declined to review a legal challenge from Cameron and Tyler Winklevoss, who claim that Facebook founder Mark Zuckerberg stole their idea for the social networking site.

The Winklevosses on Monday lost their bid for a rehearing of a 9th Circuit U.S. Court of Appeals ruling that upheld the $65 million settlement they reached with Facebook in 2008. In a brief order, the 9th Circuit without comment refused to have an 11-judge panel review the case.

Legal experts had said the appeal was a long shot.

That leaves the U.S. Supreme Court as the last hope for the Winklevosses.

The Winkevosses declined to comment. Their attorney Jerome Falk could not be immediately reached for comment.

Facebook in a statement said: “We’re pleased with the court’s decision.”

Last month, the 9th Circuit ruled that the Winklevoss twins cannot undo the settlement agreement that gave them $20 million in cash and stock now valued at more than $100 million. The Winklevosses say they were misled about the value of the stock.

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.