States say they will appeal the dismissal of their Facebook antitrust suit.

More than 40 state attorneys general on Wednesday said they planned to appeal the dismissal of their antitrust lawsuit against Facebook, setting up a protracted legal fight to rein in the power of the Silicon Valley giant.

The states would be pushing back on a decision made last month by a federal judge who eviscerated their arguments that Facebook had obtained a monopoly through its acquisitions of Instagram in 2012 and WhatsApp in 2014 and had harmed competition. The judge said that the regulators’ attempts to break up the social media company came too many years after the mergers were approved.

“The court is aware of no case, and plaintiffs provide none, where such a long delay in seeking such a consequential remedy has been countenanced in a case brought by a plaintiff other than the federal government,” the judge, James E. Boasberg of the U.S. District Court for the District of Columbia, said.

The state attorneys general have 90 days from the date of the notice to file their appeal, including their arguments.

Mr. Boasberg also dismissed a similar complaint brought by the Federal Trade Commission, criticizing the agency’s claims of monopolization, but he directed the agency to rewrite its lawsuit. The F.T.C. is expected to resubmit its lawsuit to the court by Aug. 19. The states’ notice of plan to appeal did not include new antitrust arguments and was filed to the United States Court of Appeals for the District of Columbia Circuit.

Facebook has vociferously refuted the state and federal regulators’ lawsuits, saying most the evidence used against the company now were presented to the F.T.C. when that agency approved the mergers years earlier. The company argues it does not have a monopoly, pointing to competition from Snap, Twitter and messaging applications.