"As the largest purveyor of digital rights management [DRM] protected music, Apple carries a large part of the responsibility for the situation in which consumers now find themselves," the petition reads.
The campaign is run by DefectiveByDesign, a branch of the Free Software Foundation that opposes the use of DRM software. The group claims that the technology deliberately cripples software and limits the rights of consumers.
The group filed its petition in response to an open letter from Jobs published in February.
Jobs said in the letter that Apple would remove its FairPlay DRM software from iTunes were it not for tight restrictions imposed by the major record labels.
FairPlay has come under fire in Europe recently because it limits the use of songs purchased on iTunes to Apple's iPod players.
The government of Norway has threatened to impose fines on Apple unless the company opens up the FairPlay format to outside developers.
Apple opposes releasing the technology and claims that doing so will enable applications that remove the DRM and leave Apple open to litigation.
DefectiveByDesign's Open Letter to Steve Jobs demands that the Apple co-founder make good on his promise by removing FairPlay from iTunes songs by independent artists.
It also asks Jobs to use his influence as Disney's largest stockholder to remove DRM from the film company's music and movie offerings.
"You can set the ethical example and be the first 'major' to drop DRM," reads the petition. "You can set the example in the region of video and movies. You have the direct power to do this."
Launched on 6 March, the petition reached its initial goal of 1,000 signatures in about five hours. The group plans to keep the petition open until 1 April, when it will be sent to Jobs along with a jester's hat.
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