Maps of Gustav's path show that it could strike southern Louisiana and other areas battered by Hurricanes Katrina and Rita in 2005.
Katrina, a Category 3 storm, flooded most of New Orleans, flattened beach towns in Mississippi and killed more than 1,800 people.
The exodus of an estimated 1.9 million people from the Louisiana coast is said to be the largest evacuation in state history. An estimated 95 percent of Louisiana's 2 million coastal residents had fled ahead of Hurricane Gustav by Sunday evening in the largest evacuation in state history, Louisiana's governor said.
Roads out of New Orleans - much of which lies below sea level - were crammed with traffic throughout Sunday.
Louisiana Governor Bobby Jindal appealed to residents: "If you're hearing this, seeing this, if you've not evacuated, please do so. There's still a few hours left."
New Orleans Mayor Ray Nagin told local TV only about 10,000 residents remained in the city, where rain began falling at sunset on Sunday.
A dusk-to-dawn curfew is in force in New Orleans, which is described as being like a ghost town. The mayor has warned looters will be sent to jail.
Crime was a major problem in the New Orleans area in the aftermath of Hurricane Katrina, which hit the city three years ago, causing disastrous floods.
He said the first storm winds could hit New Orleans at daybreak on Monday and Hurricane Gustav could reach Category Four strength.
Dangerous storm surges of 10 to 14 feet above normal tides are expected near and to the east of Hurricane Gustav's center, forecasters said. Rain accumulations between 6 to 12 inches are possible over parts of Louisiana, Mississippi and Arkansas, with isolated amounts of up to 20 inches, through Wednesday morning, according to forecasters.
Gustav killed at least 51 people in southwestern Haiti and eight in the neighboring Dominican Republic last week before moving to Cuba. It was in the Caribbean on Friday and intensified just before it hit Cuba.
The US Republican party's convention has been scaled back as nearly 2m people flee Hurricane Gustav, which is now nearing New Orleans.
Senator John McCain, due to accept his party's nomination for president, said it was no time for party politics.