The Queen has sent a message to President Bush saying she is "shocked and saddened" at devastation caused by Hurricane Katrina in the southern US.
Rescuers are desperately trying to reach survivors
"My sympathy goes to you and the people of the United States, especially to the families of those who have lost their lives," she said.
Foreign Secretary Jack Straw said it was "merciful" that there had not been any reports of British casualties.
Twenty Britons were among 20,000 people sheltering at New Orleans' Superdome.
The US authorities are planning to evacuate the sports stadium after conditions there deteriorated, but Mr Straw said: "Our latest information is they [the Britons] are safe.
"Obviously their circumstances are very difficult."
He added: "We have had no reports of any British deaths and that is merciful given the scale of this natural disaster."
Hundreds of people are now feared dead in the state of Mississippi and the mayor of New Orleans, in Louisiana, says he fears the dead there could number "hundreds, most likely, thousands".
British officials in Atlanta, Houston and Washington were "doing all they can to assist", Mr Straw said.
"That is our duty and will remain so."
UK relatives were having difficulty contacting family members living or visiting affected areas because power cables and telephone networks were down.
Rosemary Bird told the BBC News website that she was worried about her 18-year-old son Stuart who she believed was "stranded at his hotel" in New Orleans.
"We do not know where he is and are very worried about the lack of food and water," she said.
Cynthia McAllister, who lives near Yeovil in Somerset, told BBC Five Live she heard on Wednesday morning that her elderly parents had been rescued from their house.
But she added: "I'm still missing a nephew in Slidell, Louisiana, and I hear that's pretty badly hit as well - and another sister who evacuated to the Superdome, and I just hear it's really a real mess down there."
Most of low-lying New Orleans is under water and, according to the city's mayor, Ray Nagin, the waters have continued to rise because efforts to plug breaches in an embankment protecting the city have failed.
The Superdome stadium is without power, and toilets are overflowing, reports say.
"It's a very, very desperate situation," Louisiana Governor Kathleen Blanco said.
She said: "Many people are being rescued and are brought to the Superdome, so the dome population is growing," she said.
"They do not have the facilities to accommodate people who are there, particularly those with medical needs."
BBC correspondent Alastair Leithead said panic had gripped New Orleans, with flood waters rising and vital supplies running out.
Helicopters and boats are being used to reach people stranded on rooftops in areas under floodwater.
The exact number of people killed so far remains unknown, as rescue teams struggle to reach the worst-hit areas.
The US Red Cross has mobilised thousands of volunteers for its biggest natural disaster effort and federal emergency teams are being dispatched to affected areas.