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The deluge of gamers trying to get back on to the PlayStation Network has caused problems for Sony.

The recently restored service had to be taken offline again briefly because of the sheer number of users trying to change their passwords.

Sony was forced to close the network a month ago when hackers gained access to members' personal details.

Since then, the Japanese electronic giant has been working to improve its security systems.

Limited service has now been restored in most countries, including the UK and United States.

Users logging on again are asked to reset their passwords. They are then sent an e-mail confirming the new credentials.

Those messages were taking time to reach some players, , because the high number of resets meant that millions of e-mails were flying around the internet.

The delay was caused by internet service providers (ISPs) "throttling the e-mails" said the message.

Further problems were caused by the huge number of users trying to log on at the same time.

To clear the backlog, the PlayStation Network was turned off for 30 minutes at a time to let admin servers catch up. Sony apologised via Twitter for its struggle to cope with "extremely heavy traffic".

Initially, the only services back online were online gaming, chat and music streaming. Users were still not able to use credit cards to buy games or other content.

The Qriocity film and music services also started to be restored on 15 May in the US and Europe. The restoration of Japanese and Asian services would begin soon, Sony said.

The company promised that its "new and additional security measures" would provide users with better protection.

It has been working with a number of external security firms to increased encryption levels and add additional firewalls.

"I'd like to send my sincere apologies for the inconvenience this incident has caused you, and want to thank you for all the kind patience you've shown as we worked through the restoration process," said Kaz Hirai, Sony's executive deputy president.

He added the company was taking "aggressive action" to resolve the security issues and was making "consumer protection a full-time, company-wide commitment".

Sony will also offer users a "welcome back" package of "premium content", including a free game.

The Japanese firm has been facing a barrage of negative publicity over the security breach, which led to the theft of personal data from around 77m accounts.

Many users were upset about the company taking two days to contact the police and almost a week to inform those people affected.

Sony hired outside specialist cyber-security firms to investigate the attack, and earlier this month blamed the online vigilante group Anonymous for indirectly allowing it.

The group has denied being involved in the theft.