Thompson claimed that the corporation had initially concentrated on Microsoft users because they make up the vast majority of web users.
"The BBC iPlayer has made programmes available to Mac users and users of other operating systems via streaming since December 2007, a move which I am told has gone down very well indeed," he wrote.
"However, the issue of download of programmes to Mac and other platforms has always been more complex for technical and rights reasons."
Thompson also said that the BBC is working on a similar system for Firefox users, but offered no news on the development of an open source iPlayer downloader.