Consensus is growing among oil producers that a supply restraint pact that started in January should be prolonged after its initial six-month term, Saudi Energy Minister Khalid al-Falih said.
"There is consensus building but it's not done yet," Falih told reporters at a conference in the United Arab Emirates.
Kuwait's oil minister Essam al-Marzouq said he expected the agreement to be extended.
"Russia is on board preliminarily ... Compliance from Russia is very good," Marzouq said.
OPEC Secretary-General Mohammed Barkindo, noting that Marzouq chairs a committee that measures compliance with the cuts, said: "It is significant that the Kuwaiti minister has come out in public and said this."
OPEC is keen that non-member producers play their promised part in supporting the group's efforts to lift prices, which have recovered to $53 a barrel from lows last year below $30.
The Organization of the Petroleum Exporting Countries and non-OPEC meet on May 25 to discuss extending the curbs that total 1.8 million barrels daily, two-thirds of that from OPEC.
OPEC sources said an internal assessment was that if they failed to extend the agreement, oil could slide back to $30-$40 a barrel.
INVENTORIES STILL HIGH
Falih said his main concern was to reduce global oil inventories, calling that "the main indicator for the success of the initiative".
While inventories held at sea and in producer countries have dropped, they remain stubbornly high in consumer regions, particularly in Asia and the United States.
The International Energy Agency said last week that inventories in industrialised countries were still 10 percent above the five-year average, a key gauge for OPEC.
OPEC seems to be encouraged by the contribution of non-OPEC producers to the output cuts.
Marzouq said there was a "noticeable increase in compliance from non-OPEC". Joint compliance among OPEC and non-OPEC in March was above 90 percent, he said.
Russia has not yet publicly committed to prolonging its curbs, although Energy Minister Alexander Novak said this month that Moscow would start consultations with producing companies about the possibility of doing so.
Marzouq said another African nation, which he did not identify, had expressed interest in joining the 24-country effort.
One hold-out for an extended deal may be Iraq. Baghdad might seek to be exempt and ask to boost its own output, the leader of the nation's Shi'ite ruling coalition, Ammar al-Hakim, told Reuters.
Speaking in Cairo, Hakim cautioned that Baghdad could ask to be exempted from taking part in the supply curbs as the OPEC member country needed its oil income to fight Islamic State.
"Given these sensitive circumstances, it is the right of Iraq to hope for an exemption by the other OPEC member states and have an opportunity to increase its production," Hakim, an influential cleric, said in an interview late on Wednesday.
"But we are with the principle of reducing the overall OPEC supply to lift prices."
Iran does not look likely to become an obstacle. The current deal granted Tehran permission to lift output, hit by Western sanctions that ended just over a year ago.
"Iran is not an issue. We know they can't raise their production much more," an OPEC source said.