Some 15,000 to 20,000 customers, which could be one person or an entire apartment building, still had no electricity Saturday.
A severe thunderstorm watch has been issued for all of the Tri-State Area through 8 p.m. Saturday, reports WCBS-TV in New York.
On Friday, severe thunderstorms Friday hindered efforts to repair the series of unexplained electrical failures, and knocked out some repaired circuits, Mayor Michael Bloomberg said. Con Edison crews also have been finding more and more damage as they inspect underground cables.
"When they've opened these manholes, they've found more damage than they thought they would find," the mayor said at a briefing Saturday.
Power has been out for some residents and businesses since Monday.
A series of heavy-duty circuits supplying an area in northwest Queens failed Monday evening, hours after the state set a record for electricity use. As temperatures rose to 100 degrees, more circuits failed Tuesday. The same happened Wednesday, even after the heat wave broke and power demand plummeted.
Con Edison hasn't been able to explain why the power distribution system failed.
On Friday, Con Edison revealed that the outage was 10 times larger than it had previously reported. The utility initially said only 2,000 customers were affected, but it provided a new estimate on Friday of 25,000, saying the earlier figure was based only on the number of people who called to complain.