Cablevision said in a statement on Thursday that 1.6 million of its customers were without power while 7,265 of the remaining 1.65 million customers who were not affected by power outages still had no access to Cablevision's service.
"Following this unprecedented event, loss of electrical power continues to be the primary cause of widespread disruptions of Optimum service," Cablevision said.
Optimum is Cablevision's brand for Internet, television and telephone services.
It said it had crews working to restore service and would continue to provide updates.
The company did not respond to questions about how the disruption would impact its financials.
Last year, Cablevision said it took a hit of $16 million because of Hurricane Irene, a storm that affected the New York area in late August 2011.
Cable operators Comcast Corp and Time Warner Cable were also having service problems.
Time Warner Cable said it has had no reports of significant damage to its network, but said it was hard to assess the situation because many of its customers have no power.
Cablevision had been due to report earnings November 1, but said on Wednesday that it rescheduled the release to November 6.
The company, which mainly serves the New York area but also has operations in Montana and Wyoming, is controlled by the Dolan family. The company also owns a newspaper and TV networks.
Rivals Time Warner Cable, Comcast Corp and Verizon Communications also said they had service problems in the wake of the storm, but these companies did not provide details as to how many customers were affected.
Analysts said they expect Cablevision to incur significant costs because of the storm.
Of all the cable companies, Cablevision has the largest percentage of their subscribers in the area hard hit, Barclays analyst James Ratcliffe said.
Wireless service providers also struggled to maintain service after the storm due to floods and power outages.
(Additional reporting by Sinead Carew; Editing by Jan Paschal)
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