New York City rationed petrol as tempers were short, lines were long and panic buying continued more than 10 days after a deadly superstorm stunned the infrastructure of America's largest city.

Mayor Michael Bloomberg said the shortages could last another two weeks and that only a quarter of the city's petrol stations were open. Some had no power and others could not get fuel from terminals.

"This is designed to let everybody have a fair chance," Mr Bloomberg said of the new system, based on even and odd-numbered registration plates, that lets drivers fill up every other day.

But Mr Bloomberg's estimate was countered by the Energy Department, which said that more than 70% of the city's stations had petrol available for sales.

The queues appeared to shrink yesterday. "It's a lot better," said Manhattan driver Luis Cruz. "A couple of days ago I waited four hours. They should have done this a long time ago."

The line to his garage was just a block and a half long. Before yesterday, some lines stretched for a mile or more.

Superstorm Sandy killed more than 100 people in several states, most of them in New York and New Jersey, and its damage has been estimated at up to 50 billion dollars (£31.4bn), making it the second most expensive storm in US history, behind Hurricane Katrina in 2005.

White House press secretary Jay Carney said President Barack Obama planned to travel to New York to see recovery efforts and meet affected families, and response teams. He visited New Jersey shortly after Sandy hit, but Mr Bloomberg asked him not come to New York because a presidential visit would complicate recovery efforts in the city.

By yesterday the Red Cross had raised 117 million dollars in donations and pledges for relief work across 10 states, the District of Columbia and Puerto Rico. The Salvation Army raised five million dollars online and by phone.

Red Cross senior vice president Roger Lowe said it would probably be the charity's largest US effort since Katrina.

Salvation Army Major Darryl Leedom said the population density of the US Northeast might require a response that surpasses Katrina in the number of people served and resources required.

The Red Cross said it had deployed nearly every emergency response vehicle in its fleet with 5,800 workers and volunteers. It has served more than 3.2 million meals and snacks and provided more than 110,000 shelter stays along with other charities and government agencies.

The Federal Emergency Management Agency said it had started to move several hundred mobile homes into New York and New Jersey for the tens of thousands who have to leave their damaged homes as winter weather arrives.

The Energy Department has said the superstorm also left more people in the dark than any other storm in US history. At the peak, more than 8.5 million homes and businesses across 21 states lost power.

As drivers waited on police-monitored lines for petrol, thousands more in the region got their power back for the first time since Sandy came ashore 12 days ago.

Still, nearly 400,000 customers were without power in New Jersey and the New York City area. President Obama, who visited the battered Jersey coast two days after the storm, said he would survey the damage from the storm in New York next week.

An angry New York governor Andrew Cuomo had blasted the local utility companies as unprepared and badly managed.

"It's unacceptable the longer it goes on because the longer it goes on, people's suffering is worse," he said on Thursday.

The firms have said they are dealing with damage unprecedented in its scope.

A new, weaker storm on Wednesday dropped a layer of wet snow and knocked out power to more than 200,000 customers in New York and New Jersey, erasing some of the progress made by utility crews.

The Edison Electric Institute, the industry's main lobbying group, has called restoring power in Sandy's wake the "single biggest task the utility industry has ever faced".

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