Moscow (CNN) -- An international backlash against Russia's anti-gay propaganda law is gathering speed, from calls for a boycott of the 2014 Winter Olympics in Russia to gay bars in Los Angeles planning "vodka-dumping" protests.
A number of bars worldwide have also stopped serving Russian vodka to protest Russia's stance on homosexuality.
The furor follows concern sparked by the Russian Parliament's overwhelming support for a new law banning "propaganda of nontraditional sexual relations around minors."
Implemented last month, after President Vladimir Putin signed it into law, it bars the public discussion of gay rights and relationships anywhere children might hear it -- and has been condemned by Russian and international rights groups as highly discriminatory.
As Russia prepares to host the 2014 Winter Olympics in the resort city of Sochi, there is also great concern about what the legislation will mean for gay athletes and visitors to the country.
The debate was stirred up this week by St. Petersburg politician Vitaly Milonov, who implemented a local, earlier version of the propaganda law in his city.
Amid word that Russia would not enforce the law during the Sochi Games, he said that all Russian laws should be enforced there, regardless of who is breaking them.
"If a law has been passed by parliament and signed by the president, the government has no right or powers to reverse it," Milonov told the Russian Interfax news agency. He repeated the comments when he spoke with CNN on Wednesday.
To boycott, or not boycott?
Human Rights Watch described the anti-gay propaganda law as "a profoundly discriminatory and dangerous bill that is bound to worsen homophobia in Russia."
Under the guise of protecting children, it will infringe on people's rights to free expression and discriminate against Russia's LGBT community, it said, as the bill was being debated.
The move should be set against a backdrop of increased attacks in Russia on members of the LGBT community and gay rights activists, it pointed out.
There have been conflicting calls from gay rights activists over a suggested boycott of the Sochi Games.
While some activists back a boycott, others argue that such a step would be counterproductive.
U.S.-based company Outsports, which supports gay sport, is among those opposed to an Olympic boycott, saying critics should focus on putting pressure on Russia's government rather than denying athletes their chance to compete.
"Instead of walking away, LGBT athletes and their nations should march into Sochi holding their heads high," an article on the Outsports website said.
The International Olympic Committee issued a statement Wednesday in response to the furor, saying the Russian government had given assurances that gay visitors would not be affected by the controversial law.
"The Games themselves should be open to all, free of discrimination, and that applies to spectators, officials, media and of course athletes. We would oppose in the strongest terms any move that would jeopardise this principle," it said.
"To that end, the IOC has received assurances from the highest level of government in Russia that the legislation will not affect those attending or taking part in the Games."
USA Track and Field, the U.S. national governing body for athletics, is treating the matter as a safety and security issue, spokeswoman Jill Geer told CNN.
But, she said, the International Association of Athletics Federations has guaranteed it will not affect the athletes in any way.
The IAAF has not yet responded to CNN's requests for comment.
'Dump Russian Vodka' campaign
In response to the recent moves in Russia, internationally syndicated U.S. sex columnist Dan Savage has started a "Dump Russian Vodka" campaign, asking bartenders and booze enthusiasts to boycott Russian vodka.
Stolichnaya CEO Val Mendeleev sent an open letter last week condemning the recent laws and reaffirming the brand's commitment to the LGBT community.
"We fully support and endorse your objectives to fight against prejudice in Russia," Mendeleev wrote. "In the past decade, (we have) been actively advocating in favor of freedom, tolerance and openness in society, standing very passionately on the side of the LGBT community and will continue to support any effective initiative in that direction."
A rainbow block of text boasting that the brand "stands strong and proud with the global LGBT community against the attitude and actions of the Russian government" now dominates the Stoli homepage.
Mendeleev added that Stoli is made from Russian ingredients, but the brand is "privately owned by SPI Group, headquartered in Luxembourg in the heart of Western Europe."
In another protest move, a petition was set up Friday on the White House's "We the People" website calling on U.S. Secretary of State John Kerry to put Milonov and member of parliament Elena Mizulina on the "visa ban list" for their role in promoting anti-gay legislation.
Mizulina was "responsible for the federal law banning gay 'propaganda' to minors and for the law banning foreign adoptions of Russian orphans by gays and lesbians," the petition states.
It had more than 5,500 signatures as of Thursday.
Another White House petition, with a few hundred signatories, calls for a U.S. boycott of the 2014 Winter Olympics "due to discrimination by Pres. Putin against GLBT."
If either petition reaches a threshold of 100,000 signatures within 30 days, the Obama administration will review and respond to it.
CNN's Phil Black reported from Moscow and Laura Smith-Spark wrote in London. CNN's Alla Eshchenko, Robert Iddiols and Chris Eldergill, and CNN Money's Emily Jane Fox contributed to this report.