Con Edison expects to restore service to the vast majority of its customers by next weekend.
It also says it's on track to restore Manhattan service by this Saturday.
The utility said customers served by underground equipment in Brooklyn also can expect power by Saturday.
Most service should be restored the weekend of Nov. 10-11. The remainder could take an additional week.
There were about 649,000 Con Edison customers without service on Thursday in New York City and Westchester County.
The Long Island Power Authority says about 678,000 customers still without power. It doesn't know when restoration work might be wrapped up.
Other utilities serving Westchester, Putnam and Rockland counties reported about 130,000 outages.
Further north, in Ulster, Orange, Sullivan and Dutchess counties, there were about 50,000 customers without power.