Parker, a director of Spotify, said that Apple may have felt threatened by the streaming service, viewing it as a competitor to its iTunes service.
In an interview with Walt Mossberg at the All Things Digital conference yesterday, the early Facebook investor said that he had been given indications from industry insiders that Apple was trying to block Spotify's expansion into America last year.
"There was some indication that that might have been happening," said Parker.
The comment prompted an awkward silence between Parker and Spotify chief executive Daniel Ek, who was appearing alongside him on the panel."
Parker then volunteered that he could "get away with saying things" that Ek could not.
Apple declined to comment on Parker's claims.
Spotify, which offers free and premium music streaming packages allowing users to access millions of digital songs, launched in the US last summer after building a strong customer base in Europe.
"It's a very small industry. But one of our core competencies is our licensing framework," said Parker, who earned over a billion dollars from Facebook's recent float on the stock market.
"We are always in negotiation. We're in constant renegotiation. In that process, you hear things. There is definitely a sense in which Apple was threatened by what we were doing."
Apple's iTunes revolutionised the way people consumed music via digital downloads, but Spotify's model involves users streaming songs on devices such as laptops, tablets and smartphones.
Parker noted that Spotify represented little challenge to Apple's business model, as "even if their music store component of iTunes went away, it wouldn't be hugely significant to their bottom line".
Mossberg asked why Apple couldn't just launch a competing service offering music streaming.
"They probably can," replied Ek. "But the value of Spotify is that we have 700 million playlists."
Parker added: "We are able to combine social with music because we have a free tier of service."
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