Story highlights A member of a U.S. rock band wipes the Russian flag between his legs

State-run media report Russia's Interior Ministry has opened a criminal case

The band left Russia Sunday, CNN has learned

Russia has opened a criminal case on an American band after one of its members stuffed the Russian flag into his pants, pulled it out his backside and whipped it between his legs, state-run news agency RIA Novosti reported Monday.

A musician told the audience "Don't tell Putin" and then tossed the flag into the audience at a concert Wednesday in Odessa, Ukraine.

RIA Novosti reported that Russia's Interior Ministry has issued a statement saying that a "specialized investigative unit" within the ministry "launched a criminal case regarding desecration of the national flag."

The band, Bloodhound Gang, left Russia Sunday, CNN learned. The musicians, known for making satirical and provocative songs, had a big hit in 1999 with "The Bad Touch."

The stunt was caught on video and posted to YouTube. It went viral in the Ukraine and Russia, and was flooded with angry Russian-language comments. Journalists later quoted the band as saying that all items that the band throws into the crowd must first pass through the bassist's pants.

The group was scheduled to appear at the Kubana rock festival this week, near the southern Russian Black Sea resort of Anapa, the news agency said, but the band was "deported."

The band told CNN that it left Russia and was not deported. They said they canceled their concert at the festival.

A member of the band's crew, who asked to not be named for security reasons, told CNN the band was attacked Saturday by Russian nationalists inside Anapa airport in Krasnodar Krai.

The band members were "beaten up" by a crowd of men who punched and kicked them, the crew member said, adding that some of the attackers had whips.

He said there were no serious injuries, and a Russian police guard was accompanying them as they waited to leave.

RIA Novosti reported Monday that Russia's Criminal Code states that "foreign nationals ... who commit a crime beyond the boundaries of the Russian Federation are subject to criminal liability in line with this code if their crime is aimed against the interests of the Russian Federation or a Russian national."

Desecration of the Russian flag can result in a one-year prison sentence, according to Russian criminal code, the news agency said.

Russian prosecutors in the Krasnodar Region have said they had begun an investigation into local music festivals, including Kubana.

Russian and Ukrainian lawmakers have also proposed permanently banning Bloodhound Gang members from entering the countries.

Earlier U.S. Ambassador to Russia Michael McFaul called the incident "disgusting" in a Twitter message but said the U.S. Constitution's First Amendment protects flag desecration.