The shocked mayor of the city, Ray Nagin, said the numbers of dead could reach into the thousands: "We know there is a significant number of dead bodies in the water." Asked how many, he replied: "Minimum, hundreds. Most likely, thousands."
Despite a monumental rearguard effort by Army engineers and National Guardsmen to plug the levees breached during the furious onslaught of Hurricane Katrina, Louisiana Governor Kathleen Blanco said the waters were continuing to rise and there was no choice but to get the remaining inhabitants out.
"We've sent buses in. We will be loading them by boat, helicopter, anything that is necessary," Governor Blanco told television reporters. "It's becoming untenable. There's no power. It's getting more difficult to get food and water supplies in."
Eyewitness reports and television pictures from the city once known as the Big Easy suggested a near-apocalyptic scene of submerged streets and buildings, fetid waters fouled by debris, sewage and oil products, and gas from broken pipes bubbling to the surface and breaking out in periodic fires. There was no food, no electricity, no drinkable water. Panicked residents punched through windows, walls and ceilings to clamber on to roofs and await rescue under the punishing summer sun.
There were reports of elderly family members telling their loved ones they had no more strength and sinking into the depths, of one wife floating the body of her dead husband through the streets atop the detached door of their home, of screaming and weeping and fights breaking out in the struggle for survival.
With communication systems almost completely cut off - no telephones, no mobiles or e-mail, and only very limited radio-to-radio contact among rescue workers - it was impossible to hazard even a guess at the death toll. Officially, about 130 dead have been counted along the length of the Gulf Coast stretching into Mississippi and Alabama, but the final figure is likely to be much higher.
A massive rescue operation was being co-ordinated by 3,000 National Guard members, with back-up from every local, state and federal agency available. The Pentagon sent five ships with helicopters, hovercraft and relief supplies, as well as eight maritime rescue teams. Civilian agencies, meanwhile, prepared to tend to refugees expected to number well over one million, if not closer to twice that. The Department of Transportation alone supplied 400 water trucks, tarpaulins, mobile homes, generators, forklift trucks and emergency food and medical supplies.
About one million people are estimated to have fled the New Orleans area before Katrina struck, but that might have left as many as 200,000 behind - many of them on the poorer and more desperate end of the social spectrum.
"The poor people that are left in the city are the people who depended on those who fled but who now have nothing left themselves," said Noel Neuberger, a native Louisianan. "They are the nursemaids, the cooks, the day labourers. They are alone and the water is backing up on them."
One of the immediate consequences of the evacuation order will be the emptying of the Superdome, the sports stadium set up as a makeshift shelter during the storm and after. With conditions there described as desperate yesterday, officials prepared to move the entire refugee population by bus to Texas.
As chaos gripped the region, so too did mounting lawlessness. One of the first places to be looted was the firearm department of a Wal-Mart superstore in New Orleans. On Canal Street, in the heart of the city's tourist district, clothing and jewellery stores were picked clean. The city's Children's Hospital was besieged by gunmen apparently interested in seizing what they could from it. "There are gangs of armed men moving around the city," New Orleans' head of homeland security, Terry Ebbert, told reporters.
In Mississippi, casinos devastated by the hurricane were invaded by locals hoping to find cash inside the slot machines.
Police and National Guard troops made some efforts to intervene, prompting numerous exchanges of gunfire and an incident in which a policeman was shot in the head. Uniformed officials were, however, under instruction to focus their efforts on rescuing survivors, and in many cases chose not to react as the looters went about their business.
The most urgent task was to try to repair the broken levee walls that allowed the waters of Lake Pontchartrain, to the north of New Orleans, to pour into the city. Members of the Army Corps of Engineers are working around the clock to drop sandbags and concrete barriers into that breach, as well as another along the 17th Street Canal at the eastern end of the city.
New Orleans is not only built below sea level, exposing it to the constant risk of flooding from the Gulf of Mexico, but is also as much as 20ft below the surface of Lake Pontchartrain. The risk is that it will fill up like a bowl - not least because the high-powered pumps that usually keep Gulf and lake water out of the city failed as a result of the 120-mph winds that battered the city on Monday.
By last night, water levels in the lower parts of the city had reached 20ft. As the tide rose there were reports of alligators and cottonmouth snakes and other swamp-dwelling wildlife reclaiming the city.
Previously unaffected areas, particularly around the French Quarter, were also beginning to fill with water. Governor Blanco described the challenge facing rescue workers as "a logistical nightmare". "The National Guard has been dropping sandbags into it [the breach], but it's like dropping into a black hole."
Some of the concrete barrier-dropping work had to be suspended overnight because the helicopters were not equipped with the appropriate slings - one of a succession of problems that may yet prove to have contributed to the city's doom.
Quite what the long-term consequences of the flooding will be remains unclear. An unnamed Army Corps of Engineers officer told local radio yesterday that "if the bowl fills" it could be six months before all the water could be pumped back out again. Mayor Nagin gave a timeframe of 12-16 weeks but said rescue "was the main priority."
Exits from the city have been badly damaged, with one key interstate - I-10 - so devastated as to be unusable. Barriers and road blocks prevented anyone not involved in the rescue operation from penetrating a perimeter roughly eight miles from the city centre.
Local radio station, 870 WWL, acted as a forum for those left behind, issuing evacuation orders and urging people to take action against the rising waters before it was too late.
The scene was no less grim on Mississippi's coast, where some smaller settlements were swept away. The high-water marks were far higher even than during Hurricane Camille in 1969, the region's previous worst natural disaster.
"There were 10- and 20-block areas where there was nothing - not one home standing," Mississippi's governor, Haley Barbour, told reporters after taking a helicopter tour on Tuesday afternoon: "90 per cent of the structures are gone."
The consequences of the hurricane are likely to be felt far and wide, not least because the Gulf of Mexico accounts for one-quarter of total US oil output. Katrina shut down an estimated 95 per cent of crude production in the area, and 88 per cent natural gas output.
Samuel Bodman, the Energy Secretary, announced yesterday that the administration would release oil from its Strategic Petroleum Reserve to try to make up the shortfall. Still, energy specialists said US consumers could expect petrol prices - already at all-time highs of around $2.75 (£1.50) a gallon - to jump as high as $4 a gallon.
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