Russia has closed the criminal case against one of the 30 crew of a Greenpeace ship who were charged with hooliganism over a protest against Gazprom oil drilling in the Arctic, the group said Tuesday.

The move, part of a Kremlin-backed amnesty, should pave the way for the other 29 crew to have their cases closed and then allow the 26 foreign nationals charged in the saga to finally leave Russia.

"The first of the Arctic 30 has today heard the good news that the Investigative Committee has closed its criminal case against them," a Greenpeace spokesman told AFP, without naming the activist.

After their criminal cases are closed, the activists will still need exit visas to leave Russia as they have never officially entered the country on their Arctic Sunrise protest ship.

"They will be free to leave Russia once they get the right stamps in their passports from the migration service," said the Greenpeace spokesman in a statement to AFP.

"We know that getting those stamps would be the best Christmas present for the Arctic 30 and we hope it can occur quickly, but until such time as they do, we cannot say when they will leave."

Russia had held the 30 crew members since September after two activists scaled an oil rig in the Barents Sea owned by Gazprom to protest against oil prospecting.

Their initial arrest came when the Dutch-flagged Arctic Sunrise was seized by the Russian security forces who winched down from a helicopter in a commando-style operation.

They were initially detained in the Arctic Circle city of Murmansk and then transferred to Russia's second city of Saint Peterburg.

It was courts in Saint Petersburg that in November ordered the release of all 30 on bail. Since then they have all been free but unable to leave the city. The Arctic Sunrise ship remains under Russian control in Murmansk.

In apparent defiance of Greenpeace, Gazprom on Friday announced it had begun oil production at the Prirazlomnaya oil rig that had been the target of the activists' actions.

Greenpeace argues that the ageing oil rig is an environmental catastrophe waiting to happen which risks ruining the pristine Arctic ecology of the southern Barents Sea where the deposit is located.

The arrest of the so-called Arctic 30 -- who hail from 18 different countries -- risked becoming another bone of contention in increasingly tense relations between Russia and the West.

A photo journalist and video reporter were among those detained. Along with the 26 foreigners, there are four Russian citizens.

But the Russian parliament however passed amendments apparently specifically aimed at allowing the "Arctic 30" to benefit from the amnesty, stipulating that cases on those charges be closed even before reaching trial or verdict.

The two jailed members of Pussy Riot punk band, Nadezhda Tolokonnikova and Maria Alyokhina, were freed on Monday after benefitting from the amnesty.

Gazprom -- already owner of the world's largest natural gas reserves and a growing presence in the oil sector -- says it planned to produce six million tonnes of crude per year (120,000 barrels per day) at the site by 2021.