The Supreme Court agreed Friday to consider whether states, or only the federal government, may investigate the lending practices of national banks.

The justices said they are stepping into a dispute between New York Attorney General Andrew Cuomo, on one side, and the federal Office of the Comptroller of the Currency and an organization that represents federally chartered commercial banks, on the other. It centers on an investigation that began in 2005 under Cuomo’s predecessor, Eliot Spitzer.