* United States cites Russian restrictions on civil society
* Group was created during earlier thaw in ties
* Working group was "not working," says State Department
* Russia regrets withdrawal, says it wants good relations (Adds State Department comments)
By Steve Gutterman
MOSCOW, Jan 25 (Reuters) - The United States has quit a U.S.-Russian forum intended to promote civil society to protest Moscow's clampdown on civil rights and public activism, the State Department said on Friday.
The Civil Society Working Group was set up during a thaw in ties after Barack Obama became president, and the U.S. pullout reflects how strains have grown since Vladimir Putin started campaigning in 2011 to return to the Kremlin.
In the past year, Russia has restricted demonstrations after a wave of opposition protests that Putin accused Washington of encouraging, and has jailed or begun prosecuting several political activists.
Putin, who started a six-year term as president in May, signed a law last month that outlaws U.S.-funded organisations deemed to be involved in political activity, and Russia has ejected the U.S. Agency for International Development, which supported groups campaigning to improve civil institutions.
U.S. Deputy Assistant Secretary of State Thomas Melia said the restrictions on civil society "called into serious question whether maintaining that mechanism (the working group) was either useful or appropriate".
He said Washington's "commitment to engage Russian civil society in support of its objectives ... remains unwavering."
In Washington, State Department spokeswoman Victoria Nuland amplified Melia's remarks, saying Putin's crackdown frustrated the work of the group.
"We remain committed to a dialogue with the government of Russia on democracy issues and human rights issues, but this particular working group was not working," she told reporters.
"It was not advancing the cause of civil society in Russia, so we will do that in other ways," added Nuland.
Putin spokesman Dmitry Peskov responded mildly, saying, "Russia sincerely wants good relations with the United States and it causes regret when we lose any format for dialogue without replacing it with another."
Efforts to reinvigorate relations after Obama's re-election have been poisoned by the fallout from the death of Sergei Magnitsky, a lawyer who had accused police investigators of stealing huge sums from the state through fraudulent tax refunds, in pre-trial detention in 2009. The Kremlin's own human rights council said he was probably beaten to death.
Last year's U.S. Magnitsky Act bars Russians accused of involvement in Magnitsky's death or of other human rights violations from entering the United States, and freezes any assets they have there.
Russia responded with a law that imposes similar measures on Americans accused of violating the rights of Russians, outlaws U.S.-funded civil society groups deemed to be involved in politics, and prohibits adoptions by the thousands of Americans who came to Russia each year seeking to take in Russian orphans.
Russia has also accused Washington of meddling for criticising the Kremlin's moves to quash political dissent.
The working group was one of about 20 in a U.S.-Russia commission announced in 2009 by Obama and Russia's then-president, Dmitry Medvedev, as ties were warming.
Melia said some issues that had been addressed by the group, such as those involving children, corruption, human trafficking and prisons, might be discussed through other channels. (Editing by Kevin Liffey and Doina Chiacu)