NEW ORLEANS -- The East Baton Rouge Sheriff’s Office reported the man sought in connection with a shooting that left a woman dead is in custody and was badly wounded in a shootout with deputies Sunday night, CBS affiliate WAFB reported.

Officials said the suspect was taken to the hospital in critical condition. His name was not released. Officials added no deputies were hurt in the shootout.

Officials reported it stemmed from an earlier incident in which two people were shot, leaving one dead and the other hospitalized with injuries. Deputies said a third person was taken to the hospital after being hit by the suspect’s vehicle.

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Police Superintendent Michael Harrison previously said none of the victims during the shooting in the French Quarter were an intended target when two other men began arguing and shooting.

Harrison said the man killed was 25-year-old Demontris Toliver. He adds that five of the victims were released from a hospital by Sunday afternoon, and four remained hospitalized with injuries that were not considered life-threatening.

Police told CBS New Orleans affiliate WWL-TV in New Orleans police were close by when the shooting occurred, and responded immediately.

Mayor Mitch Landrieu said the suspects are believed to be from out of town. He called the gun violence “completely unacceptable.”

Harrison said the violence happened despite an increased police presence for the Bayou Classic football game Saturday night between Southern and Grambling universities. The New Orleans Saints played Sunday at the Superdome. He said officers were nearby, heard the shots and ran toward them.

Glean Williams, who was selling hats and other items at a table a block away from the shooting, told NOLA.com/The Times-Picayune that people ran into doorways and hotels, or hid behind palm trees decorated with Christmas lights along nearby Canal Street.

“It was panic,” said Williams, 24. “Everybody started running. People getting run over, stepped on, knocked over.”

Harrison asked that anyone witnessing the shooting to call police so “we can hold those accountable who committed this heinous crime and prosecute them to the fullest extent of the law.”