Police said the suspect, 19-year-old Akein Scott, remained at large but had been identified by multiple people.
"The time has come for him to turn himself in," New Orleans Police Superintendent Ronal Serpas said.
Police earlier had released photos that they said showed a suspect in the shooting.
The image singling out the suspect did not clearly show a face, and police, who released the photographs on YouTube, asked for the public's help in identifying and finding the person. A 10,000 dollar reward was offered for information that might help find the shooter.
The photographs, taken from a surveillance video, first show crowds of people in a street, and then the crowd is seen scattering and ducking. The final image focuses on what appears to be a man in a white shirt leaving the scene on foot as other people are lying on the pavement.
Ten men, seven women and a girl and a boy, both 10 years old, were shot when one or more people opened fire at the parade on Sunday. It was unclear if the victims were marching in or watching the parade.
Serpas earlier on Monday said he has not ruled out that the shooting was gang-related.
Violent crime in New Orleans ranks above the national average in FBI surveys. A poll of residents in 2010 found crime to be their greatest concern.
Residents gathered Monday evening with religious leaders and Mayor Mitch Landrieu at the site of the shooting to voice their anger and discuss solutions for cutting crime.
"To all the young people who are committing the violence... I don't understand why jail is such a cool place to be. You're a coward," said Jessica Strange, a social worker.
Many of the people at the outdoor meeting had also attended the parade, which the sponsoring neighbourhood club said it hoped to hold again in June depending on permits.
"We all came out here to basically reclaim this spot and to say what happened yesterday on this spot does not reflect what the people of New Orleans are or what we are about," Landrieu said.
"Yesterday was a symbol of a much, much deeper problem ... and the people of New Orleans are here today to say it's unacceptable and has to stop," the mayor said. "Nobody out there is at fault but everybody is responsible."