The outage started Christmas Day and went into Friday, PlayStation and Xbox said on their Twitter feeds, adding that they were working to restore service.
A new Twitter user going by the name "Lizard Squad" took credit for the disruption, claiming it had the "nation on strings."
The name is the same used by a group of hackers that has targeted Sony in the past, though it was not possible to verify the Twitter account's authenticity. The account did not return request for comment and only became active Wednesday.
After initially cancelling the December 25 release of "The Interview", Sony backtracked and brought it out in a few US theaters and made it available online -- including through the Xbox console and, soon, the PlayStation.
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Sony's @PlayStation Twitter account said today: "We're aware that some users are having issues logging into PSN - engineers are investigating."
https://support.Us.Playstation.Com/ -- showed that the PlayStation network status remained offline early today, a day after the difficulties began.
Meanwhile, Microsoft on a site for its Xbox customers pleaded with its customers to be patient.
"We're aware of this issue, and we're working to find a fix ASAP! We appreciate your patience in the meantime, and we encourage you to retry signing in when you get a chance. We'll update you as soon as we know more," the message said.
Xbox said on Twitter it could not estimate when service would return, while users vented their frustration with the outage online.
A major cyber attack on PlayStation in 2011 saw personal details from 77 million customers stolen, preventing customers from playing online and forcing Sony to disable the network for more than three weeks.