State, federal, and local governments are working together better than in 2005, David Paulison, the current Fema head, says.
"We've changed the culture of this organisation," he told a news conference on Saturday.
This time around, Fema began evacuating residents from New Orleans before the storm actually made landfall, lining up hundreds of buses and some chartered aircraft to assist in the effort.
Many residents confirm the early stage of the evacuation has been more orderly than Katrina.
However, a plan to electronically log and track evacuees with a bar code system failed and was aborted to keep the buses moving.
"For everyone thinking they can ride this storm out, I have news for you: that will be one of the biggest mistakes you can make in your life"
Ray Nagin, mayor of New Orleans
Officials said information on evacuees would be taken when they reached their destinations.
At least 30,000 residents of the city have requested assistance to leave.
About 10,000 people left the city by train or bus by late Saturday, officials said, with the rest expected to leave on Sunday.
Al Jazeera's Cath Turner, reporting from New Orleans, said: "A lot of [the evacuees] are going to East Texas. Texas has agreed to take 45,000 residents by car and 10,000 more by flights if necessary."
"Some are going to Baton Rouge, which is about a 45-minute drive."
About 1,000 people have also left Memphis, Tennessee, Fema said.
The agency has promised to provide emergency shelter, including mobile homes and apartments, to people displaced by the storm.
"We don't want to end up like we did with Katrina, putting people in those travel trailers," Paulison said. "That was not a good place to live for that period of time."
Law and order collapsed in New Orleans after Hurricane Katrina, with widespread looting and police officers abandoning their posts. To safeguard against a similar occurrence, Louisiana has placed 1,500 National Guard troops in New Orleans.
Gustav is expected to make landfall on Monday afternoon and may have equal or greater strength than Katrina by the time it hits the Gulf coast.
Forecasters at the US national hurricane centre said they were surprised at how quickly Gustav gained strength. It went from a tropical storm to a category four hurricane in just a day, and was likely to become a category five storm - with sustained winds of 250kph or more - on Sunday.
Ray Nagin, the mayor of New Orleans, ordered a mandatory evacuation of the city late on Saturday.
"For everyone thinking they can ride this storm out, I have news for you: that will be one of the biggest mistakes you can make in your life," Nagin said.
He said the city will not offer emergency services to those who choose to stay behind and that there will be no "last resort" shelter as there was during Katrina, when thousands suffered under squalid conditions inside the enclosed Superdome stadium.
|At least 10,000 New Orleans residents left the city on Saturday [AFP]
The state of Louisiana's largest city sits astride the Mississippi river, about 170km upstream from the Gulf of Mexico.
During Katrina, floodwalls and earthen levees across the city - meant to hold back the surging Mississippi - failed and burst, in one of the worst civil engineering disasters in US history.
Federal officials say the levees protecting New Orleans are stronger now but still have gaps that make vulnerable some of the neighbourhoods hardest hit by Katrina's floods.
Nagin said levee reconstruction on the west bank of the city is still incomplete.
A storm surge of between four-and-half to six metres would pour through canals and flood the area, as well as the neighbouring Jefferson Parish, he said.
Officials have warned Gustav's storm surge could possibly churn waves up to eight metres above normal, overwhelming some levees that held fast during Katrina.
The city's newly installed pumps and floodgates will also be put to the test.
"There's immense pressure right across the board ... this is an election year and the Bush administration will be closely watched to see how they handle this hurricane and any impending disaster," Turner said.