WASHINGTON — The Supreme Court on Monday unanimously ruled against a protester who said his free speech rights had been violated when Secret Service agents arrested him after he made critical remarks about the Bush administration’s war policies.

The case arose from a 2006 visit by Vice President Dick Cheney to a mall in Beaver Creek, Colo. A Secret Service agent assigned to protect the vice president said he heard a man standing nearby say into a cellphone that he planned to ask Mr. Cheney “how many kids he’s killed today.” The man, Steven Howards, later approached Mr. Cheney and said the administration’s “policies in Iraq are disgusting.”

Mr. Howards also touched Mr. Cheney on the shoulder. Mr. Howards said the gesture was an openhanded pat. Secret Service agents described it as a forceful push. Writing for the court, Justice Clarence Thomas said the dispute over the manner of the touch “does not affect our analysis.”

One agent, Virgil D. Reichle, later confronted Mr. Howards and asked him if he had assaulted the vice president. Mr. Howards falsely denied having touched Mr. Cheney, saying, “If you don’t want other people sharing their opinions, you should have him avoid public places.”