The Organization of the Petroleum Exporting Countries, Russia and other producers agreed late last year to cut 1.8 million barrels a day from production to stabilize prices. So far, oil has stabilized above $50 per barrel, even with increased U.S. production and continued stockpiling of supply.
In response to a question on whether the market was rebalancing in the face of large U.S. supply, Barkindo said: "It depends who you talk to and it depends on what inventories you are looking at."
"But overall, I think so far, so good. Inventories are responding if you look at both onshore and offshore inventories."
The oil industry has been hoping to get more insight from Barkindo and others this week about whether OPEC and Russia will continue to hold back production. U.S. shale drillers, meanwhile, have used the steady, higher price to bring production back on line, to a level of 9 million barrels a day, according to last week's U.S. government data.
Barkindo said the May OPEC meeting is too far away to be able to predict whether the producers would extend their deal. "That's a long time in this market," he said.
Before the May meeting, the monitoring committee, which includes Russia, will meet March 25 in Kuwait.
"When we meet in May, we'll be able to look at the numbers and see where they are. We are talking about stock levels and stock draw downs ... to what extent we achieved our [goal]," he said.