Keith Klein and Eileen Blair among homes destroyed by fire in the Breezy Point section of Queens. More Photos »

The New York region began the daunting process on Tuesday of rebuilding in the aftermath of Hurricane Sandy, a storm that remade the landscape and rewrote the record books as it left behind a tableau of damage, destruction and grief.

The toll — in lives disrupted or lost and communities washed out — was staggering. A rampaging fire reduced more than 100 houses to ash in Breezy Point, Queens. Explosions and downed power lines left the lower part of Manhattan and 90 percent of Long Island in the dark. The New York City subway system — a lifeline for millions — was paralyzed by flooded tunnels and was expect to remain silent for days.

Accidents claimed more than 40 lives in the United States and Canada, including 22 in the city. Two boys — an 11-year-old Little League star and a 13-year-old friend — were killed when a 90-foot-tall tree smashed into the family room of a house in North Salem, N.Y. An off-duty police officer who led seven relatives, including a 15-month-old boy, to safety in the storm drowned when he went to check on the basement.

On Tuesday, the storm slogged toward the Midwest, vastly weaker than it was when it made landfall in New Jersey on Monday night. It delivered rain and high winds all the way to the Great Lakes, where freighters were at a standstill in waves two stories tall. It left snow in Appalachia, power failures in Maine and untreated sewage pouring into the Patuxent River in Maryland after a treatment plant lost power.

President Obama approved disaster declarations for New York and New Jersey, making them eligible for federal assistance for rebuilding. “All of us have been shocked by the force of mother nature,” said the president, who plans to visit New Jersey on Wednesday. He promised “all available resources” for recovery efforts.

“This is going to take some time,” he said. “It is not going to be easy for these communities to recover.”

There was no immediate estimate of the losses from the storm, but the scope of the damage — covering more than a half-dozen states — pointed to billions of dollars. Gov. Chris Christie of New Jersey called it “incalculable.”

Rescuers looked for survivors in the wet rubble in places like Atlantic City, and state and local officials surveyed wreckage. Utility crews began working their way through a wilderness of fallen trees and power lines. And from Virginia to Connecticut, there were stories of tragedy and survival — of people who lost everything when the water rushed in, of buildings that crumbled after being pounded hour after hour by rain and relentless wind, of hospitals that had to be evacuated when the storm knocked out the electricity.

The president spoke with 20 governors and mayors on a conference call, and the White House said the president would survey damage from the storm with Mr. Christie on Wednesday. Mr. Obama’s press secretary said the president would join Mr. Christie, who has been one of his harshest Republican critics, in talking with storm victims and thanking first responders.

Mayor Michael R. Bloomberg said Mr. Obama had also offered to visit the city, “but I think the thing for him to do is to go to New Jersey and represent the country.”

Connecticut, New Jersey and New York reopened many closed roads and bridges, and the New York Stock Exchange made plans to resume floor trading on Wednesday after a two-day shutdown, its first because of weather since a blizzard in 1888.

There were no traffic signals on the walk from Fifth Avenue to the East River. Police officers were directing traffic; here and there, bodegas were open, selling batteries and soft drinks. In Times Square, a few tourists walked around, though some hotels still had sandbags by the doors.

Mr. Bloomberg said 7,000 trees had been knocked down in city parks. “Stay away from city parks,” he said. “They are closed until further notice.”

The mayor also said that trick-or-treating was fine for Halloween, but the parade in Greenwich Village had been postponed. The organizers said it was the first time in the parade’s 39-year-history that it had been called off.

New York’s subway network, which suffered the worst damage in its 108-year-history, faced one of its longest shutdowns because the problems were so much worse than expected, said Joseph J. Lhota, the chairman and chief executive of the Metropolitan Transportation Authority, the agency that runs the subways and several commuter railroads.

Water climbed to the ceiling of the South Ferry subway station, the end of the No. 1 line in Lower Manhattan, and debris covered tracks in stations up and down other lines after the water rushed in and out. Mr. Lhota said that seven subway tunnels between Manhattan and Brooklyn were flooded.

He also said that the Metro-North Railroad had no power north of 59th Street on two of its three lines, and that a 40-foot boat had washed up on the tracks in Ossining, N.Y.

The Long Island Rail Road’s West Side Yards had to be evacuated, and two railroad tunnels beneath the East River were flooded in the storm. The railroad had not restored power on Tuesday and had no timetable for restoring service. The Brooklyn-Battery Tunnel, officially the Hugh L. Carey Tunnel, and the Queens-Midtown Tunnel also remained impassable, he said.

Airports, too, took a beating. More than 15,000 flights were canceled, and water poured onto the runways at Kennedy International Airport and La Guardia Airport, both in Queens. Officials made plans to reopen Kennedy, the larger of the two and a major departure point for international flights, on Wednesday. Gov. Andrew M. Cuomo said La Guardia would remain closed “because of extensive damage.”

The flooding in the tunnels in Lower Manhattan was so serious that the Federal Emergency Management Agency asked specialists from the Army Corps of Engineers to help. The “unwatering team,” as it is known — two hydrologists and two mechanical engineers from the corps with experience in draining flooded areas — flew to the airport in White Plains because it was one of the few in the area that was open.

Buses began running again on Tuesday afternoon, and the mayor ordered a ride-sharing program for taxis. He said more than 4,000 yellow cabs were on the streets by Tuesday afternoon.

From southern New Jersey to the East End of Long Island to the northern suburbs in Connecticut, power companies spent Tuesday trying to figure out just how much damage the storm had done to their wires, transformers and substations.

The work will take at least a week, possibly longer, because the damage was so extensive, and utility companies called in thousands of crews from all around the country to help out. Consolidated Edison reached to San Francisco to bring in 150 workers from Pacific Gas and Electric.

Even with the additional manpower, Con Edison said it could still take more than 10 days to complete the repairs. Con Edison had more than 285,000 customers in Manhattan who were in the dark on Tuesday, and more than 185,000 in Westchester.

Things were worse east of New York City, where nearly one million customers of the Long Island Power Authority did not have power on Tuesday and Mr. Cuomo made clear he wanted the authority to restore power faster than it had in the past. He said it was “not O.K.” for it to take two weeks to repair lines brought down by tree limbs.

In New Jersey, Public Service Electric and Gas said it had 1.3 million electric customers in the dark, including 500,000 without power because a surge in Newark Bay flooded substations and other equipment. Another New Jersey utility, Jersey Central Power and Light, whose territory covers many shore towns, said almost all of its customers had lost power in some counties, including Ocean and Monmouth. More than one-third of Connecticut Light and Power’s 1.2 million customers had no electricity, either.

The fire in Breezy Point, Queens, leveled scores of houses, among them one that belonged to Representative Bob Turner, who was riding out the storm at home despite the mayor’s order to evacuate low-lying areas. Mr. Turner’s spokeswoman, Jessica Proud, said he and his wife made it out safely after flames reached their house. Michael R. Long, the chairman of the state Conservative Party, had a home nearby that also burned down, she said.

Flooded streets in the area prevented firefighters from reaching the blaze, a Fire Department spokesman said, and the mayor, who toured the area on Tuesday afternoon, said the neighborhood was devastated.

“To describe it as looking like pictures we have seen at the end of World War II is not overstating it,” the mayor said.

The off-duty officer who drowned in his basement was identified as Artur Kasprzak, 28, who was assigned to the First Precinct in Manhattan. He had led seven relatives upstairs to the attic as the water rose in his house on Doty Avenue on Staten Island. He said he was going to check the basement and would be right back. About 20 minutes later, one of his relatives called 911 and said he was missing.

A rescue team with boats and motorized water scooters tried to answer the call but could not reach the house at first because power lines were in the water. His body was found shortly before sunrise.