Sony has won over some gamers by offering free access to its PlayStation Network to compensate for the leak of personal details on 78 million user accounts, but still has some way to go to regain the trust of consumers.

Many PlayStation users around the world were angry and frustrated that the first warning of one of the largest Internet security break-ins ever came a week after Sony detected a problem with the network on April 19.

Sony on Sunday apologized and said it would gradually restart the PlayStation Network with increased security and would offer some free content to users.

Analysts warned restoring customers' faith would take time -- a blow to the consumer electronics giant that has touted online services as a way of leveraging its strengths in both hardware and content, including films and music as well as games.

Damage has been done to Sony whatever the scale of the content giveaway at this point, and Sony is facing a prolonged effort to regain customer trust, said Jay Defibaugh, director of equities research at MF Global in Tokyo.

Anything that undermines consumer willingness to divulge credit card details to Sony is a problem for the network strategy, he added.

Sony said on Sunday it would offer some free content, including 30 days of free membership to a premium service to existing users and in some regions pay credit card-renewal fees. Compensation would only be paid if users suffered damage, it added, without providing details.

The news sparked thousands of comments on the PlayStation blog and Facebook page, many of them supportive.

It's nice to know that Sony have such a level of care and respect for their Consumers, said a user under the name Ragabunny. I honestly never doubted Sony for a second over this...As a Playstation owner since the first console,I've always been aware of how good they are at recognizing problems within their infrastructure and the gaming world.

Others expressed dissatisfaction.

The point is you took our money and didn't secure our credit card and personal data. I'm not even sure how you can possibly make up for that, said a post by a user under the name rawstory.

Some users said they would be unwilling to register their credit card details in future.

However personally I am never placing my CC (credit card) info in your hands again, if I ever buy anything off the PSN (PlayStation Network) it will be through pre-paid cards, said a PlayStation user under the name leukoplast.

Shares in Sony closed up 2.5 percent to 2,316 yen, outperforming the broader Nikkei index, but falling short of rival Nintendo, which ended up 4.1 percent. Sony shares fell as much as 5 percent on Thursday as concerns mounted about the impact of the breach.

Analysts said the leak would weigh on investor sentiment.

At minimum, having to suspend the service, fix its problems and deal with the aftermath, looks set to cost (Sony) tens of billions of yen, said analyst Nobuo Kurahashi of Mizuho Investors Securities.

I don't think anyone knows where they will be able to absorb this loss, nor how much it will be, and that'll weigh on share prices going ahead, he added.

Goldman Sachs estimated the total earnings impact would be less than 50 billion yen ($615.5 million). Many users open multiple accounts and the total number of valid credit cards registered on the network is 10 million, with other gamers using prepaid cards.

The incident has sparked legal action and investigations by authorities in North America and Europe, home to almost 90 percent of the users of the network, which enables gamers to download software and compete with other members.

(Editing by Joseph Radford and Lincoln Feast)

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