Michael Bloomberg said in a statement: “We would not want a cloud to hang over the race or its participants, and so we have decided to cancel it.”
Plans to press ahead with the race had prompted uproar from politicians in cyclone-ravaged parts of the city.
More than 90 US deaths, over 40 of them in New York, have been blamed on Sandy.
Across the US East Coast, some 3.5 million homes and businesses – 1.2 million in New York state alone – still have no electricity, four days after the storm made landfall.
Mayor Michael Bloomberg said in his statement: “While holding the race would not require diverting resources from the recovery effort, it is clear that it has become the source of controversy and division.”
He added: “We cannot allow a controversy over an athletic event – even one as meaningful as this – to distract attention away from all the critically important work that is being done to recover from the storm and get our city back on track.”
It was not immediately clear if the race would be rescheduled for another date.
Elected officials representing Staten Island were among the harshest critics of Mayor Michael Bloomberg’s earlier statements that the race would go ahead.
“We’re still pulling bodies out of the water and the mayor is worried about marathon runners and returning to life as normal,” US Representative Michael Grimm, who represents the island and part of Brooklyn, told CNN.
“The Verrazano Bridge should be used for getting fuel and food in to Staten Island, not getting runners out. Police resources would be best allocated to prevent looting and in rescue and recovery operations.”
Rep Michael Grimm was joined by other local politicians, including both Republicans and Democrats, in demanding the race be postponed.
“The decision to move forward with the marathon is not a decision I would have made,” City Council Speaker Christine Quinn said.
Some runners who have signed up for the race told local website Gothamist that they would volunteer on Staten Island instead.
There was further controversy when background music played at the marathon expo in a Manhattan convention centre included the heavy metal song, Rock You Like a Hurricane.
Manhattan Borough President Scott Stringer, who originally wanted the race to go on, said on Friday that he had changed his mind.
“New Yorkers deserve nothing less than to know that the entire government is focused solely on returning the city and their region back to normalcy,” Scott Stringer said in a statement.
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