A 24-year-old American photographer serving a six-year sentence for cocaine smuggling flew to the United States Monday in the custody of U.S. marshals to serve the rest of his term, authorities said.

Conan Owen of Annandale, Va., was turned over to the marshals who accompanied him on a commercial flight that left Barcelona's El Prat international airport bound for New York, a police spokesman said.Owen was sentenced in April to six years and a day in prison and fined $18,000 for smuggling nearly $200,000 worth of cocaine into Spain in the false bottom of a suitcase.

A Barcelona judge refused to accept a confession by a drug trafficker at a U.S. federal court that Owen had been framed.

U.S. Embassy press attache Robert Meade said he did not know where Owen would be taken.

"It is now in the hands of the Department of Justice. That is all I know," Meade said.

The Socialist government approved Owen's transfer Oct. 28 under a 1983 agreement between the European Community and the United States that allows prisoners to serve terms in their own countries.

The case attracted wide attention in the Spanish news media, which accused the Reagan administration of putting pressure on Spain to acquit Owen.