The justices did not comment Tuesday in refusing to disturb the convictions and sentences of life in prison.
Defense lawyers had argued the men were innocent fishermen who had been abducted by pirates and forced to fire their weapons at a U.S. Navy ship.
But the government said that the Somalis had confessed to attacking the USS Nicholas after mistaking it for a merchant ship. The Nicholas, based in Norfolk, Va., was part of an international flotilla fighting piracy in the seas off Somalia.
The court also rejected a separate appeal from another group of Somalis who have yet to be tried on piracy charges.