Police are looking for one Akien Scott who has previous arrests on charges of possession of firearms, possession of narcotics and resisting arrest, New Orleans Police Chief Ronal Serpas announced Monday night.
"I would recommend strongly that Mr Scott contact anybody who he is comfortable with to turn himself in," Serpas was quoted as saying by CNN.
When asked if Scott was the lone shooter, Serpas said it was still early in the investigation.
Images of the parade, released by police Monday, show a man standing at the outskirts of a packed parade route. A moment later, he charges toward the crowd.
The dramatic surveillance camera images see the panicked crowd scrambling for cover. The man runs away, leaving scattered bicycles and bodies on the ground behind him.
Federal investigators cited by CNN said they have no indication that the shooting was an act of terrorism.
"It's strictly an act of street violence in New Orleans," New Orleans FBI spokesperson Mary Beth Romig said Monday.
The shooting, during a festive New Orleans Mother's Day parade, renewed concerns about crime in the city known as the home of jazz.
It's the third holiday this year when guns have been fired into crowds, New Orleans Mayor Mitch Landrieu said.
"It's a culture of violence that has enveloped this city for a long period of time ... and it's one of the things that we as a community have got to stop," he was quoted as saying.
A Jan 21 shooting near a Martin Luther King Day parade left five wounded. Four people were hurt in a February Mardi Gras attack, the New Orleans Times-Picayune reported.
Authorities are offering $10,000 reward in the case. Remi Braden, a police spokesperson, described the shooting as "an extremely unusual occurrence".
The attack included shots that were fired from different guns, police said Sunday, and officers saw three possible gunmen running from the scene.
On Monday, at least three victims were in critical condition, said Louisiana State University Medical Center spokesman Marvin McGraw.