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."
Al Jazeera's Cath Turner in New Orleans said that so far the city's levees, which had failed during Katrina, appeared to be holding.
So far there have been reports of only minor flooding and damage.
The US Army Corps of Engineers said on Monday that the federal flood protection system protecting New Orleans should hold as the hurricane hits.
But the corps also said this did not mean there would be flooding, and images on Monday showed waves overlapping at least one levee in the city.
The storm is expected to swamp parts of the states of Louisiana, Mississippi, Arkansas and Texas with up to 30cm of rain and 50cm in some areas.
Hurricane Gustav has already caused widespread damage in the Caribbean, hitting the Dominican Republic, Haiti, Cuba and Jamaica and leaving more than 80 people dead.
|McCain said Monday's Republican convention activities would be curtailed [AFP]
Ray Nagin, the mayor of New Orleans, cautioned against complacency, saying: "We are nowhere near out of danger yet."
"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 have 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 have 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, Missouri 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.
Oil companies have also 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.
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.
"I can't take a chance because so many people died in Katrina"
Vanessa Jones, New Orleans resident
Gustav's approach stirred uneasy comparisons to 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.
Long lines of cars and buses streamed out of New Orleans on Sunday after the evacuation was ordered.
One resident, Vanessa Jones, 50, said she had planned to stay but changed her mind after watching the news all night.
"I can't take a chance because so many people died in Katrina," she said as she prepared to board a bus headed to an unknown destination.
Harvey E Johnson, the US deputy emergency agency chief, said evacuees who didn't have relatives to stay with were being housed in junior college dormitories away from the anticipated disaster area.
Flights from New Orleans and other Gulf Coast cities were cancelled on Monday as the storm bore down on the region.