"Since yesterday to this time, light has come back to about 70,000 more customers across the city," Bloomberg told a news conference.
He said about half of those still without power were in Manhattan but added that there should be electricity on most of the island by midnight Friday.
More than 250,000 people had power cut on Monday night when Sandy caused an explosion at a substation near the East River.
Con Edison, the New York power company, made automatic telephone calls to some Manhattan customers on Friday saying their electricity has been restored, but called back an hour later saying "this is an important announcement: please disregard our last message."
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