* Putin's decree allows rallies in approved zones in Sochi
* IOC welcomes decision to ease restrictions
* Putin has staked his reputation on Winter Olympics (Edits, adds IOC comment, more background)
By Vladimir Soldatkin
MOSCOW, Jan 4 (Reuters) - President Vladimir Putin has eased curbs on demonstrations in the Winter Olympics venue of Sochi in a gesture likely to burnish Russia's image ahead of an event dogged by security and human rights worries.
Keenly aware that the success or failure of the Games will help shape his legacy, Putin has closely identified himself with the $50 billion project. He made a surprise inspection of venues in the Black Sea resort on Friday and was shown on Russian state television skiing down a slope in dark glasses and a helmet.
Putin, who on Saturday attended a rehearsal of the Games' opening ceremony in Sochi, amended a decree to allow groups to hold some marches and gatherings at sites approved by the security services, the Kremlin said in a statement.
"Gatherings, rallies, demonstrations, marches and pickets, which are not directly connected to the Olympic and Paralympic Games, could be staged on Jan.7-March 21 2014... only after agreeing with... a local security body," it said.
Campaign groups, calling for everything from gay rights to political reform, have complained that the ban on rallies, imposed in August as part of a security crackdown, violated Russia's own constitution.
Putin's move came shortly after he ordered a further security clampdown following two suicide bomb attacks in the southern Russian city of Volgograd which killed at least 34 people.
No one has claimed responsibility for the blasts, but they were a reminder of the continuing threat posed by militants who want to carve an Islamic state out of a swath of southern Russia that includes Sochi.
The International Olympic Committee welcomed Putin's decision, the latest in a flurry of gestures apparently aimed at disarming critics of Russia's human rights record.
"It is in line with the assurances that President Putin gave us last year and part of the Russian authorities' plans to ensure free expression during the Games whilst delivering safe and secure Games," it said in an emailed comment to Reuters.
There was no immediate reaction from human rights groups.
Putin wants to use the Olympics to showcase what he regards as Russia's political and spiritual revival under his firm leadership after its loss of superpower status with the 1991 fall of the Soviet Union and the economic turmoil of the 1990s.
In a gesture to Western and Russian critics who accuse him of crushing dissent, Putin last month freed several of Russia's best known prisoners: former oil tycoon Mikhail Khodorkovsky and two members of the female punk group Pussy Riot.
Rights groups have criticised Russia's treatment of migrant workers, particularly on Olympic sites, and have called for a boycott of the Games over a law banning the spread of "gay propaganda" among minors, saying it violates basic freedoms.
A December opinion poll showed Putin's public approval rating fell to its lowest level in more than 13 years against the backdrop of high inflation and a weaker economy. (Additional reporting by Karolos Grohmann; Editing by Gareth Jones)