Russia rights group law 'backward-looking': Greenpeace chief

* Greenpeace calls on Putin not to implement new law

* Legislation has sparked international, domestic criticism

MOSCOW, Aug 14 (Reuters) - A new Russian law that brands rights groups that receive funding from overseas "foreign agents" is "a backward-looking step", the global chief of Greenpeace said on Tuesday, calling on President Vladimir Putin not to implement it.

The new legislation, signed into law by Putin in July , has been criticised by the United States and by Russian rights activists who say the term "foreign agent" smacks of the Cold War and is aimed at discrediting them.

It was introduced at a time when Kremlin critics say Putin, who returned to the presidency in May for the third time, is pushing ahead with a crackdown on dissent. Fines for protesters have been increased, Internet regulation has been tightened, and stricter rules for defamation have been brought in.

"Let us not use a legislative intervention that is so weak, so backward-looking and so anti-democratic that it will actually embarrass Russia in the international community should this actually continue to be implemented," Executive Director of Greenpeace International Kumi Naidoo said in Moscow.

The Russian unit of Greenpeace falls under the new law since it receives funding from Greenpeace International.

"This is a regressive step," Naidoo told a news conference. "It sends a very negative picture of how the Russian government sees certain parts of civil society."

Under the new law, foreign-funded non-governmental organisations dealing with "political activity" are obliged to register with the Justice Ministry as "foreign agents" and file a report to officials every quarter.

The penalties for failing to comply include six months' suspension without a court order and, for individuals, up to three years in jail.

Russia has angrily rebuked foreign criticism, calling it "gross interference" in its domestic affairs. It says the new law improves transparency of public life.

Activists say a court verdict concerning an anti-Kremlin protest by the punk rock group Pussy Riot should give a fresh indication of how much dissent Putin is willing to tolerate. The verdict is expected on Friday. (Reporting by Gabriela Baczynska; Editing by Andrew Osborn)