Saudi Arabia's oil minister Ali al-Naimi and his Russian counterpart Alexander Novak will meet in the Qatari capital Doha, where they will be joined by ministers from OPEC members Qatar and Venezuela.
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The meeting revives memories of a 2001 encounter between OPEC and non-OPEC producers when OPEC heavyweight Saudi Arabia pushed through a global deal to curb output in which Russia agreed to participate for the first and last time.
However, Moscow never properly followed through on its pledge to curb exports.
Oil prices rose 2 percent on the news on Monday in trade thinned by a US holiday.
They have fallen to their lowest in more than a decade over the past year due to booming US supplies and a decision by OPEC to ramp up exports which was aimed at driving higher-cost producers out of the market.
Saudi Arabia has said it would cut output only if non-OPEC producers agreed to join it.
Russia, the world's top producer, has long refused to cooperate, saying its industry was competitive at any price and it was technically challenging for Moscow to reduce production.
The mood started to change in January as oil prices fell below $30 per barrel - a fraction of what Russia needs to balance its budget as it is heads towards parliamentary elections later this year.
Public finances in Saudi Arabia and other Gulf states are also suffering badly.
OBSTACLES TO DEAL
Industry sources told Reuters last week some OPEC countries are trying to achieve a consensus among the group and key non-members for a production freeze, in an attempt to tackle the global glut without cutting supply.
Several Russian officials, including Novak, have signalled that cooperation with OPEC was possible.
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The head of state oil major Rosneft Igor Sechin - an ally of President Vladimir Putin who had long spoken against the cuts - said last week it would make sense for all producers to remove around 1 million barrels per day from the market.
He did not say if Moscow was ready to contribute, while Putin has yet to speak on the subject.
Nigeria's oil minister told Reuters the mood inside OPEC was shifting to a growing consensus that a decision must be reached on how to prop up prices.
Many analysts, including the International Energy Agency, are sceptical OPEC will cut a deal with other producers to reign in ballooning output, however.
"We continue to believe that if prices were to be artificially supported with production cuts it would only give more expensive forms of production more room to breathe and would only solve the problem in the short term," Phillip Futures said in a note.
Many OPEC watchers said the biggest obstacle to an OPEC/non-OPEC deal would be the positions of OPEC members Iran and Iraq. Both have indicated they plan to raise production this year, although there was no indication either would participate in Tuesday's meetings.
The meetings are taking place in Qatar - this year's holder of the rotating OPEC presidency, giving it a role in coordinating consultations among members and suggestions for extraordinary meetings of the group.
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