Napster has offered $1bn to settle a copyright infringement lawsuit that threatens to shut it down.
The offer was announced a week after a federal appeals court said the music industry will almost certainly win its lawsuit against the pioneering digital entertainment company.
"We all ought to sit down and settle this case as fast as we can," Napster chief executive Hank Barry said.
However, an industry group instead urged Napster to accept a federal injunction ordering it to block copyrighted music from its service.
"This path would be more productive than trying to engage in business negotiations through the media," said Hilary Rosen, president of the Recording Industry Association of America.
In the court judgment, a three-judge panel of the 9th US Circuit Court of Appeals ordered Napster to stop millions of users from swapping copyrighted music without charge and without restriction.
Napster, whose lawyers have said such action would be virtually impossible, has vowed to appeal.
It has argued it is not to blame for how subscribers use copyrighted material, citing a 1984 case in which the Supreme Court refused to hold VCR manufacturers and videotape retailers liable for people copying movies.
But the appeals court said no such protection extends to Napster because the company knew users were swapping copyrighted songs.