The figure is down from the 400 listed as missing on Sunday and the 131 still unaccounted for yesterday, when Foreign Office officials said some were likely to have died in the storms and flooding.
"The numbers are coming down," the foreign secretary, Jack Straw, said today. "We are working very hard with officials in the US and here to give every assistance we can. It is an uncertain situation, and we are doing all we can to help."
Lord Triesman, the foreign minister, said consular teams were in the affected areas attempting to trace missing Britons.
"We have been going to every address where we believe there might be British citizens, not just in New Orleans but Louisiana and Mississippi," he said.
"Most of the people that have been accounted for in the past 24 hours have been found in this way."
He said most of those found over the past day were long-term residents, and that officials were in "repeated contact" with worried families.
"Of the 96, I do not think many are visitors," Lord Triesman told the BBC's World At One. "We felt yesterday that most short-term visitors had been located and, while I cannot be 100% confident, I am pretty confident we are dealing with people who are long-term residents now."
He said some British citizens had decided to stay with their properties in the devastated areas.
One Briton had been found on the porch of his home with his dog and had "no intention of leaving", Lord Triesman added, saying there had yet to be any confirmed British casualties.
A Louisiana police official said the Red Cross and other charities were compiling lists of names of people at shelters.
British survivors continued to arrive back in the UK today, many to emotional receptions. Student Michelle Andrews' parents Stephen, a 46-year-old college lecturer, and Sharon, a 44-year-old hairdresser, ran through the arrivals hall at Gatwick airport to greet her.
The 20-year-old said police in New Orleans had told her to "fend for herself" among dead bodies and men toting guns in the hours after the disaster.
"It was absolutely terrifying, and I feared for my life", the student, from Pontyclun, Wales, said. "We were on the 17th floor of a hotel in the centre of New Orleans when the hurricane hit. We were warned to expect the windows to blow in. We just lay down in the corridors as these thick white clouds just closed in on us. It was hell."
Penny Rounce, who was among those reported as missing, finally managed to contact her parents almost a week after the disaster.
The 22-year-old fashion student had emailed her family just before the hurricane struck, but was then trapped in the New Orleans Superdome.
Her mother said it was only after she and several other white girls had become the target of what they claimed was racial abuse that they were escorted to a medical centre.
"There is no doubt that she owes her life to the National Guard," she said. "By Thursday, it was so ugly in there. She was getting abused and bottles were being thrown at her. She said they were the centre of the abuse because they were white. The black people thought they [white people] were getting preferential treatment."
Among those still believed to be missing are Mike Noone, a British engineer who helped design part of the space shuttle.
Other Britons yet to make contact with their families include 48-year-old Mike Healy, originally from Warwickshire but now living in Bay St Louis, Mississippi. His sister, Susan Betteridge, 52, of Stratford-on-Avon, is planning to fly out to look for him.
Jill Amend, 70, from Richmond, south-west London, was waiting for news of her son, Vernon Carroll, 46, who she fears she may have seen floating face down in the flooded city on television news.
"I know he would call me if he could," she said. "I wish the Foreign Office could be a bit more supportive ... all I can do is sit here, wait and worry."
