Coast Guard Vice Adm. Thad Allen, head of the federal disaster relief effort, said Saturday that Nagin's idea is both "extremely ambitious and "extremely problematic."
But Nagin said his plan was developed in cooperation with the federal government and balances safety concerns and the needs of citizens to begin rebuilding.
"We must offer the people of New Orleans every chance for a sense of closure and the opportunity for a new beginning," he said.
CBS News Correspondent Sharyn Alfonsi reports that this weekend,
"We're being told by the mayor to come back in and open your business," Lee Page, a New Orleans resident and business owner, told Alfonsi. "My insurance company is telling us that it might be three months before they even come and look at our house."
Nagin said the Algiers, Garden District and French Quarter sections would reopen over the next week and a half, bringing back more than one-third of the city's half-million inhabitants. City officials later backed off setting a specific date for reopening the famous French Quarter, the city's main tourist draw.
Allen said a prime public health concern is the tap water, which in most of the city remains unfit for drinking and bathing. He said he was concerned about the difficulties of communicating the risk of using the water to people who return and might run out of bottled water.
Another concern is the risk of another storm hitting the region, threatening an already delicate levee system and possibly requiring residents to be evacuated again, he said.
Allen, who planned to meet with Nagin on Monday, said federal officials support the mayor's vision for repopulating the city, but he is concerned about the mayor's timeline.
"Our intention is to work with the mayor...in a very frank, open and unvarnished manner," he said.
Business owners were allowed back in to some sections of the city to begin the long process of cleaning up and rebuilding, part of Nagin's plan to begin reviving the city by resuming a limited amount of commerce.
But confronted with damage that could take months to repair, many said hopes for a quick recovery might be little more than a political dream.
"I don't know why they said people could come back and open their businesses," said Margaret Richmond, owner of an antiques shop on the edge of the city's upscale Garden District that was looted. "You can't reopen this. And even if you could, there are no customers here."
The Wal-Mart store in uptown New Orleans, built within the last year, survived the storm but was destroyed by looters.
"They took everything, all the electronics, the food, the bikes," said John Stonaker, a Wal-Mart security officer. "People left their old clothes on the floor when they took new ones. The only thing left are the country-and-western CDs. You can still get a Shania Twain album."
Algiers, a residential area located across the Mississippi River from downtown New Orleans, is scheduled to reopen Monday, the first neighborhood to welcome back residents. Uptown, including the historic Garden District neighborhood, also is scheduled to reopen this week.
All the areas to be reopened this week were spared Katrina's flooding. Electricity and clean water have been restored to some sections.