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Asche said his group was "extremely disappointed" and expressed that feeling to Viacom.
An MTV spokesman said the network declined to comment.
The VMAs are MTV's biggest event of the year and the show was seen Sunday by nearly 10 million people across several of Viacom's networks. Cyrus sang a song, "Dooo It!" that included the lyrics, "Loving what you sing, and loving smoking weed." She ate supposed pot brownies with Snoop Dogg in one skit, and lit up with a group of friends in another. She held up a selfie stick and encouraged the group of people behind her, "Everyone say marijuana!"
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Pot is popular among MTV's target audience. College students are smoking marijuana at a higher rate than at any time in the last 35 years, surpassing cigarette smoking, according to a University of Michigan study released this week. A Pew Research Center poll from this spring found that 53 percent of American support legalizing pot, a percentage that rises to 68 percent among people born between 1981 and 1997.
The message sent by celebrities about marijuana on the VMAs is every bit as persuasive as the show's commercials, said Tim Winter, president of the Parents Television Council.
"What they're basically doing is telling everyone, especially kids but all viewers, that marijuana use is nothing to eschew," Winter said.
Plenty of successful people smoke pot, and have the financial cushion to handle it if things go wrong, said Kevin Sabet, head of the anti-drug group Smart Approaches to Marijuana. Not everyone in MTV's audience has the same luxury.
"It's really a bad message to young people that marijuana is harmless," Sabet said, "especially at a time when the marijuana kids are using is 5 to 10 times as strong as the marijuana their parents used."
Asche's Truth Initiative has been operating since 2000 to target young people about the dangers in cigarette smoking. Noticing that tobacco products like hookah and flavored cigars are on the rise, it produced a special commercial targeting those areas.
Backstage as she offered a hit to photographers, the 22-year-old Cyrus noted that she'd been smoking for a while.
"Because you're all my friends, and my song is kinda, sorta about the love of marijuana and the love of humankind, I brought a little joint if anyone would like any," she said. "Anyone?"