The city's emergency preparedness director said residents may be allowed to return 24 hours after the strong winds die down.
The latest hurricane comes three years after New Orleans was devastated by Hurricane Katrina.
On Monday, water flooded over the top of the city's Industrial Canal floodwall, but city officials and the US Army Corps of Engineers said they were "cautiously optimistic and confident" the walls would hold.
George Bush, the US president, described the hurricane on Monday at a news conference as a "serious event" but said "I feel good [that] the co-ordination on this storm is a lot better than during Katrina".
"Gustav doesn't have no punch - I went through Katrina and this is totally different, it's weak"
Randall Dreher, New Orleans resident
Reports say that scores of homes in the city were damaged, with roofs torn off and flooding damage. Power outages were also reported in up to 20 per cent of the state.
"Gustav doesn't have no punch," builder Randall Dreher in New Orleans told the Reuters news agency. "I went through Katrina and this is totally different. It's weak."
The hurricane is expected to slow considerably as it heads towards Texas and possibly Arkansas, where both states could be soaked with up to 50cm of rainfall.
Gustav hit the US as a new hurricane, Hanna, formed in the Caribbean and forecasters predict it could hit the southern US states of Georgia and South Carolina late in the week.
A new tropical storm, Ike, also formed late on Monday afternoon in the Caribbean.
Gustav caused widespread damage in the Caribbean, hitting the Dominican Republic, Haiti, Cuba and Jamaica and leaving more than 80 people dead.
Its approach sparked comparisons to Hurricane Katrina, the most costly hurricane in US history, which killed about 1,500 people and caused more than $80bn in damage almost exactly three years ago.
Ray Nagin, the mayor of New Orleans, cautioned against complacency, saying: "We are nowhere near out of danger yet."
|McCain curtailed events at the
Republican convention [AFP]
"Those canals are full right now. I don't know if we are going to get any more water pushed in that direction but that is a big concern for me right now."
Officials said there was enough food, water, ice and other supplies stockpiled for one million people over the next three days.
Fewer than 10,000 people remained in New Orleans, according to reports, while police and several thousand national guard troops patrolled the city in a bid to prevent looting.
More than 11 million residents in five US states had been threatened by the fast-moving storm.
John McCain, the US presidential nominee for the Republican party, said most activities planned on Monday for the first day of his party's convention in Minnesota would be suspended because of the hurricane emergency.
"I hope and pray we will be able to resume some of our normal operations as quickly as possible," McCain said while visiting a disaster centre in Waterville, Ohio, during campaigning.
Gustav had also forced oil companies to shut down nearly all production in the energy-rich Gulf of Mexico, a region that normally pumps a quarter of US oil output and 15 per cent of its natural gas.
But US crude oil futures slipped to below $115 a barrel on Monday morning as fears of major damage to oil facilities in the Gulf of Mexico eased.
Prices had hit more than $118 per barrel in a special trading session on Sunday.