Ukrainian President Petro Poroshenko and his Russian counterpart Vladimir Putin had spoken by telephone and discussed measures to restore peace in eastern Ukraine, Kremlin reports.
They are expected to continue discussions on the conflict as well as on the gas dispute on the sidelines of a summit of European and Asian leaders they are both attending in Milan on Oct 16-17.
Russian natural gas producer Gazprom cut supplies to Ukraine in June after Kiev failed to pay gas debts which Russia says have now reached more than $5 billion.
Ukraine faces a possibility of energy shortages this winter if no deal is reached, risking a replay of the disruptions to Europe's gas supplies seen in 2006 and 2009. Europe receives a third of its gas needs from Russia, and around half of it is pumped via Ukraine.
Officials from Russia and the European Commission, which is mediating the talks, say a deal could be near. Poroshenko said on Saturday he hoped for "significant progress" on the issue during the talks on Milan.