Saudi Arabia has long denied responsibility for the attacks and pointed to a finding by the 9/11 Commission that it had found no evidence that the Saudi government "as an institution" had involvement.
But the issue has refused to go away.
Cozen, which has taken the lead in the litigation, sued the kingdom in 2003 in U.S. District Court in Manhattan, alleging that Saudi-funded Islamist charities had secretly provided money and logistical support to al-Qaeda for more than a decade.
In 2005, a federal District Court judge in Manhattan ruled that Saudi Arabia could not be sued. The court said the kingdom could not be held accountable for what the charities did with the money.
Ruling in 2008, the U.S. Court of Appeals for the Second Circuit agreed that Saudi Arabia could not be the target of a terrorism lawsuit. But in December, the Second Circuit effectively reversed itself and reinstated the kingdom as a defendant.
The Saudi government appealed that ruling, and the Supreme Court on Monday refused to hear it, without comment.
Carter said he expected that discovery of Saudi government documents and depositions would begin shortly.
Cozen represents dozens of insurers that suffered losses as a result of the destruction of the World Trade Center.
Other plaintiffs in the litigation include the family of John O'Neill, a former senior counterterrorism official at the FBI, who sounded some of the first alarms about Osama bin Laden and died in the attacks on the World Trade Center, where he had gone to work as head of security after leaving the FBI.
"The O'Neill plaintiffs believe that the Supreme Court correctly denied . . . Saudi Arabia's petition seeking review of the Second Circuit's decision reinstating it in the 9/11 litigations," said Jerry Goldman, a lawyer with the firm of Anderson Kill P.C., which represents the O'Neill family. "We are looking forward to proceeding with discovery."