By Sonia Elks

(Reuters) - Russian rights activists said on Monday they would draft a list of the country's most flagrant human rights violators to help the United States identify individuals it could systematically deny U.S. visas under a new law.

U.S. President Barack Obama infuriated Moscow on Friday when he signed legislation to "name and shame" Russian rights violators, a move Russian President Vladimir Putin called an insult.

Washington named the new law after Sergei Magnitsky, a Russian lawyer working for a Western private equity firm who died in a Russian jail in 2009. The legislation also obliges U.S. banks to freeze the assets of Russian citizens allegedly involved in Magnitsky's death and other broad-ranging abuses.

Inspired by the Magnitsky Act, veteran rights campaigner Lyudmila Alexeyeva on Monday announced the creation of a new group she said would investigate claims of abuse by the police, prosecutors and other Russian officials with a view to publishing their names.

Its establishment is likely to further anger the Kremlin, which has faced Western criticism over a crackdown on dissent, that has included the arrests of opposition demonstrators and criminal cases against protest leaders since Putin's return to the Kremlin for a third term in May.

Alexeyeva said she hoped the list would help the U.S. authorities identify people they wanted to punish under the new legislation.

"We can say: ‘Look we have this project - if you consider it noteworthy, add it to the Magnitsky list'," said Alexeyeva, 84, a doyenne of Russia's rights movement who has been challenging the authorities since the start of the Soviet dissident movement in 1960.

"Our dream is that later, our violators ... will be punished within our own justice system. Until that happens, I personally am grateful to the U.S. congress," she said.

The new group will be made up of rights activists as well as a retired Constitutional Court judge and a TV personality and will seek volunteer lawyers to help with investigations and donations to fund its work.

Activists says Russia's human rights record is poor. Problems they cite include homophobia, violence against women, sexism, xenophobia and the opposition says there are still political prisoners in the country's jails - a charge the Kremlin denies.

Describing the Magnitsky Act as an insult, Putin has said that Washington had no right to try to take the moral high ground and dictate to its former Cold War foe on human rights, a sphere he argues has become highly politicized.

On Friday, Russia's parliament hit back, giving preliminary approval to its own tit-for-tat measure to deny visas and freeze the assets of Americans deemed to have violated the rights of Russians abroad.

(Reporting By Reuters trainee Sonia Elks; Editing by Alissa de Carbonnel and Andrew Osborn)