The US government says it is now in control of New Orleans, six days after Hurricane Katrina wrought havoc.
Homeland Security Secretary Michael Chertoff said troops had secured the city and that full relief operations were under way.
Visiting the Louisiana city, Defence Secretary Donald Rumsfeld said it could take years for the city to recover.
The US has given the EU and Nato a list of specific emergency aid it needs for the relief operation.
American officials have asked for blankets, first aid kits, water trucks and food.
EU Environment Commissioner Stavros Dimas said the union was ready to offer whatever assistance it could, while Nato said it too was ready to help.
A number of European countries have already pledged financial help individually, and member countries of the International Energy Agency, have agreed to release oil reserves. Kuwait has offered $500m of oil products.
Earlier, US Health and Human Services Secretary Michael Leavitt said the death toll from Katrina would be in its thousands - the first such acknowledgement by a federal official.
In a series of interviews, Mr Chertoff defended the government's response to the disaster amid allegations that it reacted too slowly.
He said the magnitude of the hurricane and flood was beyond all expectations, and had "exceeded the foresight of the planners and maybe anybody's foresight".
As the search for bodies moved to the forefront following rescue operations that have seen thousands evacuated from the city, Mr Chertoff warned of grim days ahead, with house-to-house searches.
"It is going to be about as ugly a scene as you can imagine," he told Fox News.
He said that with the additional National Guard and regular troops sent to New Orleans, there was "no question... we've secured the city", following an outbreak of lawlessness that saw looting and reports of murders and rapes.
In a sign that the Bush administration was moving on to a public relations offensive, Mr Rumsfeld inspected military relief efforts in New Orleans on Sunday, while Secretary of State Condoleezza Rice toured Mobile, Alabama, another storm-hit area.
Mr Rumsfeld described the death and destruction caused by the hurricane as a natural disaster of historic proportions.
"It will take many, many, many months, and into years, for this area to recover to the circumstances it was in," he told reporters at New Orleans airport.
Meanwhile, a statement on the internet, purportedly from al-Qaeda in Iraq, called the destruction divine punishment of the United States.
The statement said God had attacked America in response to the prayers of the oppressed.
Thousands of people have finally been evacuated from the New Orleans Superdome complex, a rallying point for survivors that saw thousands left for days in squalid and dangerous conditions.
Up to 40 aircraft flew around the clock to move the survivors to safety.
The BBC's James Coomarasamy in New Orleans says huge swathes of the city remain completely submerged while, in other areas, the streets are deserted.
He says on the main inter-state highway, convoys of speeding emergency vehicles share space with small groups of people pushing their belongings in shopping trollies and hoping for a lift to safety.
Utilities experts are due to enter the city for the first time to assess the damage caused by the hurricane and the failure of New Orleans' flood defences.
More than one million people are said to have been displaced from their homes in Louisiana, Mississippi and Alabama. Most of them are in Texas, Tennessee, Indiana and Arkansas.