NEW NEWS
BBC correspondents say most of those who wanted to leave have done so, but some are determined to stay.
The authorities have vowed to restore security in the Louisiana city following a breakdown of law and order.
President George W Bush is due to visit Louisiana and Mississippi - his second trip to the region in three days.
The BBC's Justin Webb in Washington says the Bush administration is now focused on being more effective on the ground in the hurricane-hit areas and on convincing Americans that the White House is not to blame for what went wrong.
The president's suggestion over the weekend that local officials made mistakes has led one Louisiana Senator, Mary Landrieu, to threaten to punch him if he says it again.
The visit follows an incident on Sunday in which US police shot eight people, reportedly killing five, after contractors escorted by officers came under fire.
A week after the hurricane struck the Gulf coast, Mr Bush's father, former President George Bush senior, and former President Bill Clinton, are due to visit Houston, Texas to launch an aid appeal for victims.
Limited return
Rescue teams have been working around the clock to move stranded survivors to safety.
Map of central New Orleans
Homeland Security Secretary Michael Chertoff said troops had secured the flood-stricken city and full relief operations were under way.
The BBC's Matthew Davis in New Orleans says the city's convention centre is littered with the debris of the thousands of people who have now left.
A huge airlift rescues thousands of survivors from New Orleans
In pictures
Chairs, barbeque grills and stained mattresses are among the discarded items lining the street for hundreds of metres.
Electricity has now been restored in some areas, and some of the first evacuees have been allowed to return briefly to their homes in the west of the city, to collect belongings.
Helicopters and boats are still looking for survivors.
Only 59 bodies have been recovered so far in New Orleans, but officials says the death toll could run into the thousands.
The authorities have issued a mandatory evacuation order.
But the BBC's Richard Greene says he met several people who were determined to stay behind.
'Ugly scene'
AP news agency also reported that some survivors were determined to stay, to defend their neighbourhood from looters.
The first few days were a natural disaster, the last four days were a man-made disaster
Phillip Holt, 51
New Orleans evacuee
Devastation at a glance
Eerie silence in New Orleans
"We kind of together decided we would defend what we have here and we would stay up and defend the neighbourhood," army veteran Charlie Hackett was quoted as saying.
But Mr Chertoff has warned that staying is not a reasonable alternative.
"We are not going to be able to have people sitting in houses... for weeks and months while we de-water and clean the city," he said.
"The flooded places, when they are de-watered, are not going to be sanitary."
"We are going to uncover people who died, maybe hiding in houses, got caught by the flood... It is going to be about as ugly of a scene as I think you can imagine."
More than one million people are said to have had to leave their homes in Louisiana, Mississippi and Alabama. Most of them have gone to Texas, Tennessee, Indiana and Arkansas.
even senators wanna start shit....
