LOS ANGELES — Jared Lee Loughner, accused of trying to assassinate Arizona Rep. Gabrielle Giffords, will be tried first on federal charges, according to an agreement announced Friday by federal and state prosecutors.

Loughner, 22, of Tucson, Ariz., has been charged in a three-count federal indictment of shooting Giffords and killing two other federal employees in an attack last month outside a Tucson supermarket where Giffords was meeting with constituents.

Six people were killed in the attack and 13 injured, including Giffords, who is recovering in a Texas rehabilitation center from gunshot wounds to the head.

Loughner has pleaded not guilty to the federal charges.

The agreement to have the federal government move first on the charges was announced by Pima County Attorney Barbara LaWall and Dennis Burke, the U.S. attorney for Arizona.

“”Since the first moments of the investigation into the tragic events on Jan. 8, 2011, our offices have worked together, and with our federal, state and local law enforcement partners, to investigate these crimes and to assist the victims and their families throughout this process,”” the pair said in a prepared statement.

“”Our offices have jointly agreed to a process that Loughner will first be prosecuted on federal charges by the U.S. Attorney’s Office. As required by the statute, once those charges have been fully prosecuted through the federal court system, Arizona state charges will be prosecuted by the Pima County Attorney’s Office. These cases will be tried in sequence and will ensure that all rights of the victims and their families are vindicated,”” they stated.