Parker said Apple clearly felt threatened by Spotify and that he had gotten indications from dealings with people inside the industry that the iPhone maker was doing its best to impede Spotify's expansion.
Reuters said that Parker answered a question at the All Things Digital conference as to whether Apple had tried to keep Spotify out of the United States.
He said that there was some indication that that might have been happening.
Parker said that he could say this because Spotify Chief Executive Daniel Ek, who was sitting beside him at the time, could not.
While Spotify did well in the UK, the music industry suddenly started dragging its feet on licensing when it tried to open its doors in the US.
In the process of Spotify's negotiations with people in the music industry, he had heard things and people sent him emails.
But he added there was definitely a sense in which Apple felt threatened by what Spotify was doing.
Parker said he was not sure why Apple was so worried. Spotify's business challenges only a small part of Apple's overall business. He said that even if the iTunes music store component went away, Apple would not lose much.