Barkindo said consultations were under way for the extension of the OPEC-led pact beyond March 2018 and that more oil producing nations may join the supply pact, possibly at the next meeting of OPEC in Vienna on November 30.
Saudi Arabia and Russian Federation are now leading consultations between OPEC and other major suppliers about the future of their agreement to cut oil output, Barkindo said on Sunday in New Delhi.
Last November, major oil producers agreed to cut output as a response to the global supply glut that had been pushing down prices for almost two years.
In a speech to the Reuters Global Commodities Summit on Monday, Barkindo said he saw clear evidence the oil market was rebalancing. Prices fell 3.3 percent last weekend are down about 2 percent this year.
Oil prices have gained support and in late September reached nearly $60 a barrel, the highest in more than two years.
Crude oil inventories were seen down by 467,000 barrels, while distillates likely declined by 1.1917 million barrels and gasoline stocks rose 967,000 barrels.
Among other bullish news for oil, Morgan Stanley cut its forecast for US crude output growth, citing a range of operational headwinds including limited availability of fracking crews.
"Just a mere 25 million barrels are products, nearly converging with the five year average", he said.
The secretary-general of Opec has claimed that the oil export organisation is close to victory in its fight to rebalance the global crude market.
"Crude in floating storage is down by an estimated 40 million barrels since the start of the year with help of a narrowing contango since June and then Brent flipping into a clear backwardation from the second week of September", he said. OPEC in its last monthly report raised its projections for oil consumption this year and next, and this development could have further to run.
OPEC is also seeing a decline in growth in United States shale oil output, whose increasing volumes helped bring about the slide in prices three years ago.
The BofA-Merrill Lynch report said US shale oil production should increase 470,000 barrels per day this year and another 690,000 barrels per day next year.