"Serious" human rights problems such as anti-gay violence are clouding the run-up to the Sochi Olympics, Human Rights Watch said Tuesday while hailing the release of Kremlin critics from jail.

"The cases of (Mikhail) Khodorkovsky, the Pussy Riot women and the Greenpeace activists are no longer casting a shadow over February's Winter Olympic Games in Sochi," HRW's Russia programme director Tania Lokshina said in a statement.

But the global New York-based rights group cited "rising homophobic violence" and "homophobic rhetoric in state media" as being among "many serious problems (that) plague Russia's rights record."

The group acknowledged however that the release of former tycoon Khodorkovsky, Greenpeace activists and Pussy Riot members from prison had improved the situation.

In the run-up to the games, Russia's rights record has come under fresh scrutiny with many critics calling on world leaders to boycott the February 7-23 Games.

The HRW report on Russia's rights situation in 2013 said Moscow had continued a "crackdown on civil society and government critics".

The group focused on a controversial anti-gay law that bans "gay propaganda" about homosexual relationships and has been harshly criticised by Western countries.

"Homophobic rhetoric, including by officials, and rising homophobic violence accompanied debate about these laws," the report said.

It detailed how "vigilante groups consisting of radical nationalists and neo-Nazis" have been luring gay people to meetings and then beating them and posting videos of the attacks on social media.

"In September 2013 a video showed the rape of an Uzbek migrant in Russia who was threatened with a gun and forced to say he was gay," the report said.

"A few investigations were launched, but have not yet resulted in effective prosecution."

At the same time, "attacks and harassment of LGBT (lesbian, gay, bisexual and transgender) activists... also increased," it said.

President Vladimir Putin, who has repeatedly denied his policies are anti-gays, said Sunday that all gay athletes and guests were welcome at the Sochi Games.

HRW raised concerns over another new law that discriminates against gay people by banning adoption by foreign same-sex couples or single people from countries where same-sex unions are legal.

These measures are "opening the door to discrimination and closing space for activism", the group said.

HRW also slammed a law that brands non-governmental organisations with international funding as "foreign agents", and a governmental campaign against migrant workers.

"The Kremlin is treating foreign-funded independent groups, LGBT people and migrants as though they were enemies of Russia," Lokshina said.