A similar service called Instant Listening provides users with access to CDs that were recently purchased at online stores.
The copyright infringement lawsuit, filed last week in US District Court in New York, seeks to prevent MP3.com from marketing the services, an RIAA spokeswoman said.
"The foundation on which these services are built is an unauthorised digital archive with the most popular and valuable copyrighted sound recordings in the world - music that is not owned by MP3.com," Cary Sherman, the RIAA's executive vice president and general counsel, said in a statement.
MP3.com created the archive without attempting to get permission from record labels or recording artists, and has therefore committed a "blatant infringement of rights," according to Sherman.
In a statement issued this afternoon, MP3.com denied any wrong doing.
"Although we haven't had an opportunity to review the complaint, we plan to defend this suit vigorously through the courts. We have every intention of fighting this to the court of last resort, if necessary," Michael Robertson, MP3.com's chief executive officer, said.
The Beam-it software on MP3.com's Web site asks users to verify that they have purchased a song in CD form before they can download a digital version of it. The RIAA asserts that the verification process is inadequate.
"That's what they ask - but there's no way to prove it," said Kerry Driver, a spokeswoman with the RIAA's public relations firm.
The RIAA is an industry group representing record companies based in the U.S.