More than 10,000 people have signed an e-petition on the 10 Downing Street website urging the BBC to make its iPlayer available to non-Windows users.
At the time of writing, 10,006 people had signed the petition calling for the prime minister to instruct the BBC to provide the iPlayer for other operating systems, such as Linux or Apple's OS X.
iPlayer is the BBC's online on-demand television service which was launched last month. It will be available for public download on 27 July — but only for Windows XP users.
At the launch of the iPlayer last month, Ashley Highfield, director of future media and technology at the BBC, said: "I'm fundamentally committed to universality. We're not favouring one platform over another."
He added: "Our general rule of thumb is to reach the biggest audiences first."
A BBC statement said it is in the corporation's interests to make its content as "widely available as possible".
The BBC added that developing a version for Apple Macs and Microsoft Vista is "absolutely on our critical path for this year".
Open-source industry group, the Open Source Consortium has been invited to meet the BBC's independent governing body — the BBC Trust — to discuss its concerns about the iPlayer.