Nagin's order targets everyone except those individuals who have been designated as helping with the relief effort.
An estimated 10,000 residents are believed to still be in New Orleans, and some have been holed up in their homes for more than a week.
Most of the people who have been reached by rescuers are grateful and glad of a chance to get out of a city that grows ever more dangerous, with germs and dead bodies in the huge stagnant pool of water that surrounds the city.
But some fear leaving the only city they know might mean a worse fate, and rescuers have reported being in personal danger confronted by holdouts who refuse to leave.
No one knows exactly how many people fit into that category.
"I think a lot of these people as you know are convinced that the water's gonna subside and get back to normalcy," Admiral Joseph Kilkenny told CBS News.
"We have to convince them to leave," said Nagin. "It's not safe here. There is toxic waste in the water and dead bodies and mosquitoes and gas. We are pumping about a million dollars' worth a gas a day in the air. Fires have been started and we don't have running water."
Acknowledging the mayor's declaration, Police Capt. Marlon Defillo said late Tuesday that forced removal of citizens had not yet begun. He said that officers who were visiting homes were still reminding people that police may not be able to rescue them if they stay.
"That would be a P.R. nightmare for us," Defillo said of any forced evacuations. "That's an absolute last resort."
Tuesday, engineers began the herculean and possibly months-long task of pumping out the flooded city, and the water level is dropping noticeably. "I'm starting to see rays of light," said Nagin.
Local officials' frustration with the Federal Emergency Management Agency's sluggish response was exacerbated however, when internal documents showed the government's disaster chief, Michael Brown, waited roughly five hours after Hurricane Katrina struck the Gulf Coast before asking Homeland Security chief Michael Chertoff to dispatch agency employees to the region: 1,000 to arrive within two days and 2,000 to show up within a week.
The New Orleans pumping began after the Army Corps of Engineers used rocks and sandbags over the Labor Day weekend to finally plug the 200-foot gap that let water spill into the city and swamp 80 percent of the bowl-shaped, below-sea-level city in the aftermath of Hurricane Katrina.
On Tuesday, the Corps said the area under water has been reduced to about 60 percent of the city.
"I'm starting to see water levels much lower than I've seen," said Nagin, said after surveying his city from the air. "Even in areas where the water was as high as the rooftops, I started to see parts of the buildings."
He warns of the horrors that are likely to be revealed when the waters recede. "It's going to be awful and it's going to wake the nation up again," the mayor predicted.
Local authorities braced for the eventual death toll.
"I said thousands. Some computer models say 10,000," New Orleans Mayor Ray Nagin told CBS News. "I don't know what the number is. But it's going to be big. And it's going to shock the nation."