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Sony says it took the network down to investigate an "external intrusion".
In a blog post, the company thanked users for their patience and assured them that it was working "around the clock" to strengthen the network infrastructure.
"Though this task is time-consuming, we decided it was worth the time necessary to provide the system with additional security," wrote Patrick Seybold, Sony's senior director of corporate communications.
As well as gaming, the outage has affected other services running over the PlayStation Network, such as the UK-based film rental site LoveFilm.
The company has confirmed that LoveFilm customers are currently unable to stream films on the service, according to the BBC. In the US, users of film streaming service Netflix have also reported problems.
Sony has admitted it does not know when the security improvements will be completed to make the PlayStation Network available again to its 70 million users.
Sony has not responded to user concerns about the security of their personal information, including credit card details stored on the PlayStation Network.