A Federal Emergency Management Agency (Fema) briefing heard that although the high water pressing the walls raised the potential for problems, officials were "confident in the resilience" of the levees.
The Mayor of New Orleans, Ray Nagin, has urged caution.
He said: "We're still seeing storm surge. There's lots of rain, tornado threats... We are nowhere near out of danger yet."
The mayor asked people to "resist the temptation to say we're out of the woods", adding that heavy rainfall could still flood the city over the next 24 hours.
He told CNN that the city would not know until late afternoon if vulnerable areas would "stay dry".
Fema officials warned that the damage wrought by Gustav would be "a catastrophe".
"We don't expect the loss of life, certainly, that we saw in Katrina," Fema spokesman Harvey Johnson said, "But we are expecting a lot of homes to be damaged, a lot of infrastructure to be flooded, and damaged severely."
In 2005, three-quarters of New Orleans was flooded by a storm surge that claimed more than 1,800 lives in coastal areas.
The Category Three storm Katrina swept away the city's levees under a wall of mud and water.
In New Orleans, a dusk-to-dawn curfew is in force.
The Louisiana National Guard has been mobilised and support requested from other states.
The storm threatened protective walls as it approached New Orleans
Crime was a major problem in the New Orleans area in the aftermath of Hurricane Katrina.
Concern for those facing the hurricane has prompted the Republican party to scale back its national convention where Senator John McCain is due to accept the party's nomination for president at the event in St Paul, Minnesota later this week.
Mr McCain told his party that "this was one of those moments in history where you have to put America first. We will not see the mistakes of Katrina repeated".
Out in the Gulf of Mexico, most oil production has been shut down. Three years ago, Hurricanes Katrina and Rita ravaged the region's oil infrastructure and sent oil prices soaring.
Meanwhile, Tropical Storm Hanna has strengthened into a hurricane east of the Bahamas in the Atlantic ocean, US officials reported.
Hanna is on track to skirt Florida before making landfall on Friday in South Carolina, near its state border with Georgia, US weather experts said.
Have you been affected by Gustav? Are you preparing for its arrival? Send us your comments and experiences using the form below.
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