The telecommunications giant said in a blog post that the law is harmful to lesbian, gay, bisexual and transgender people and harmful to a diverse society.
"We support LGBT equality globally and we condemn violence, discrimination and harassment targeted against LGBT individuals everywhere," AT&T said in the post.
AT&T said it was responding to a request from the Human Rights Campaign, which urged International Olympic Committee sponsors to stand up for LGBT equality. AT&T isn't an IOC sponsor, but says it supports the campaign's principles.
AT&T is the first major U.S. corporation to publicly condemn Russia's law, Human Rights Campaign officials said.
The Washington-based organization that pushes for civil rights for LGBT people called AT&T's move courageous.
"AT&T should be recognized for showing true leadership in opposing this hateful Russian law and other sponsors that have failed to lead should take corrective action immediately," the campaign said in a post on its website. "A company that claims to support LGBT equality should do so wherever it operates, not just in the United States."
The law, signed by President Vladimir Putin in July, bans pro-gay "propaganda" that could be accessible to minors. Activists view the measure as forbidding almost any public expression of gay-rights sentiment. The law has extensive public support in Russia, where it cleared parliament virtually unopposed.
Activists have pressed the IOC and Olympic sponsors to denounce the law and call for its repeal, launching a campaign in July with a boycott of Russian vodka.
The IOC and top sponsors have expressed opposition to discrimination in general and pledged to ensure that people gathering for the Olympics wouldn't be affected by the law.
A coalition of 40 international groups, including the Human Rights Campaign along with Amnesty International and Human Rights Watch, sent an open letter to the 10 biggest Olympic sponsors last week urging them to run ads promoting equality for LGBT people.
On Tuesday, Human Rights Watch posted a video on YouTube of gay people being bullied, chased and beaten, compiled from footage the group said was uploaded by perpetrators. The video got more than 700,000 views in less than two days.
A New York group planned demonstrations Wednesday in 19 cities worldwide, including St. Petersburg, Jerusalem and Rio de Janiero, the site of the 2016 Summer Games, to urge Olympics sponsors to speak out against the law.
Oskar Garcia can be reached on Twitter at http://twitter.com/oskargarcia
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