Storm-battered New York got slowly back on its feet on Wednesday, with Wall Street and two of the city's airports up and running after a monster storm that left more than 50 Americans dead.

Just six days before America goes to the polls, President Barack Obama surveyed the damage in neighboring New Jersey, where tens of thousands of homes are under water and millions of families without power.

"You guys are in my thoughts and prayers. We are going to be here for the long haul," Obama promised during a visit to an emergency shelter in Brigantine, near Atlantic City, with New Jersey Governor Chris Christie.

"We're going to not tolerate any red tape. We're not going to tolerate any bureaucracy. We're going to make sure that we get the help to you as quickly as we can," Obama said, adding that military aircraft were available to help move emergency repair crews around.

While much of New York and many more towns along the US East Coast remained paralyzed following Monday's onslaught by superstorm Sandy, the New York Stock Exchange got back to work.

John F. Kennedy and Newark Liberty airports also made a limited reopening and LaGuardia was to follow suit on Thursday. At last count, 19,500 flights had been cancelled because of Sandy, tracking service flightaware.com said.

Buses were back on New York streets and state Governor Andrew Cuomo announced that limited subway services would resume Thursday, although flooding and power outages kept large parts of the network immobilized.

Limited commuter rail service to New York suburbs resumed Wednesday, while Mayor Michael Bloomberg announced temporary car pooling rules to reduce the gridlock choking Manhattan.

Institutions returning to service also included the UN Security Council, which suffered flooding from the East River.

Despite these improvements, large sections of New York, including many skyscrapers in lower Manhattan, remained without electricity, and schools throughout the city were to remain shuttered for the rest of the week.

Bellevue Hospital, the oldest in the country, decided to evacuate its remaining 500 patients on Wednesday after flooding inundated the basement and knocked out electricity.

In nearby Hoboken, on the New Jersey side of the Hudson River, people in flooded homes were still waiting for rescue, while in Jersey City, a night curfew was declared in the wake of looting.

Obama said authorities were also focusing on New York's Long Island and Connecticut, where many seaside communities were flooded, as well as West Virginia, where the massive storm dumped a blanket of snow in remote areas.

The presidential election campaign, which went into a hiatus during the storm, was likewise coming back to life in the final run-up to election day on November 6.

Obama, who had suspended his re-election campaign but was constantly in the headlines as he responded to Sandy, arrived in New Jersey in the early afternoon to tour devastated areas.

The Democratic president won glowing public praise for his handling of the situation from Christie, an outspoken Republican and a key backer of his party's candidate, Mitt Romney.

Romney gingerly returned to the campaign trail in the key swing state of Florida, but he too addressed the plight of storm-battered Americans hundreds of miles to the north.

"So please, if you have an extra dollar or two, please, send them along and keep the people who have been in harm's way... in your thoughts and prayers," he told about 2,000 people in an airport hangar in Tampa.

As the scale of the disaster sank in, about 10,000 National Guard troops deployed to storm-hit states to help local authorities rescue stranded survivors, remove debris, direct traffic and assess the damage from the air, the Pentagon said Wednesday.

While National Guard trucks rolled through the flooded streets of New Jersey, troops offered help along a main highway in the mountains of snow-struck West Virginia.

Army engineers stood ready to provide pumps and generators as needed while the US Navy sent out three amphibious ships off the New Jersey coast in case state governments requested aid for rescue operations.

New York police raised the storm-related death toll to 24 on Wednesday, with the overall US toll passing 50, according to officials. Another 67 people died as Sandy swept through the Caribbean last week.

As of Wednesday, nearly two million customers had electricity restored, but another 6.2 million across 16 states remained without power, the Department of Energy said.

Insured losses from Sandy could run between seven and 15 billion dollars (5.4 to 11.5 billion euros), according to initial industry estimates.

Four nuclear power reactors remained shut after storm waters wreaked havoc with transmission networks and cooling systems, but authorities said there were no risks to the public. One of the reactors, at New Jersey's Oyster Creek plant, was removed from an "alert" status.

Meanwhile, the annual New York marathon was confirmed to be going ahead on Sunday after doubts about whether roads would be cleared in time and whether thinly stretched police would have sufficient resources.

However, another Big Apple tradition, the Halloween Parade on Wednesday evening, was postponed.