"The service will be resumed in the foreseeable future," said an AllofMP3 statement published online. "We are doing our best at the moment to ensure that all our users can use their accounts, top up balance and order music."
Kvasov was the general director and owner of the Media Services, the company behind the site, which charged extremely low prices for music downloads and was the UK's second most popular paid-for download site, behind Apple's iTunes.
The Cheremushkin District Court in Moscow found in favour of Kvasov, though presiding judge Yekaterina Sharapova said that this was because of a lack of evidence caused by a 'sloppy' prosecution case.
"The prosecution did not succeed in presenting persuasive evidence of his involvement in infringing copyright law," said Sharapova in her ruling. She said she wanted to "draw attention to the sloppy job done by prosecutors in collecting and analysing the facts," and said prosecutors should be "careful in collecting evidence in connection with intellectual rights violations".
Kvasov's legal team argued that he was a director of the company in a period before a law change during which it was legal to make recordings available. The law changed to outlaw it only in September 2006, said his lawyers.
Recording industry associations in the US and Europe have argued that AllofMP3 is illegal because it operates without the permission of or payment to their members.
AllofMP3 says that it makes payments to artists through collections society the Russian Multimedia and Internet Society (ROMS), but that the record labels do not accept those payments.
Music on AllofMP3 is cheaper than on services such as iTunes sometimes by a factor of 10. Popular, recently-released albums were available for as little as $1.
Since AllofMP3 was closed down another near-identical site, MP3Sparks.com, opened. Two other current directors of Media Services face charges relating to AllofMP3 in cases that are yet to be heard.
Three major labels, EMI, Warner and Universal, had been seeking 15 million roubles, or around £293,000, in the case against Kvasov.
AllofMP3 has been a prominent stumbling block in negotiations about Russia's joining of the World Trade Organisation. US trade officials have said they would block Russia's entry while sites such as AllofMP3 were allowed to operate unpunished within its borders.
Earlier this year a 25 year old man was arrested in London and is suspected of being AllofMP3's agent in the UK, selling vouchers for tracks from the site.
