Michael Wohl, executive director of the New York City-based group, said he believed the album was the reason for the iTunes interruption, though he had no proof.
"We issued a release saying that over 40 (Olympic) athletes downloaded the album in an act of solidarity, and that's what triggered it. Then everything got blocked," Wohl said by phone.
Beijing encourages Internet use for education and business use but tries to block access to foreign sites run by dissidents and human rights and Tibet activists.
The Ministry of Industry and Information Technology, which regulates Internet use, did not respond to a request for comment. A spokeswoman for the Ministry of Public Security said she had no information.
Apple, based in Cupertino, Calif., acknowledged that customers were having trouble.
"We are aware of the log-on problems but we have no comment at the moment," said Huang Yuna, an Apple spokeswoman in Beijing. She declined to say how many customers were believed to be affected.
Blocked iTunes users poured out their frustration on Internet bulletin boards.
"It seems like suspending iTunes is punishment for iTunes, but really it doesn't hurt iTunes, it hurts us," said a note on macfans.com.cn, a Chinese site for Apple users.
The Dalai Lama has been vilified by Chinese authorities, who claim he is trying to split Tibet from China. He says he only wants greater autonomy for the Himalayan region to protect its Buddhist culture.
Violent protests broke out in March in the Tibetan capital of Lhasa. Many Tibetans insist they were an independent nation before Communist troops invaded in 1950, while Beijing says the Himalayan region has been its territory for centuries.
Wohl said his group contacted Olympians ahead of the games and offered free copies of the 20-song album. He said those who downloaded it included competitors from the United States, Canada, Britain, Spain, France and Australia.
Most got the album before entering China, but "some in Beijing did download, and I think that's what spooked the Chinese government," Wohl said.
Wohl declined to identify the athletes by name, saying he wanted to avoid making trouble for them with the Chinese government or the International Olympic Committee.
China has the world's largest population of Internet users, with 253 million people online as of June, according to the government. The United States is in second place with 223.1 million people online, according to research firm Nielsen Online.
Apple has no China-based iTunes service. Users must log on to sites for the United States or other markets. Despite that, the company's iPod digital music player is hugely popular in China.