Saudi Arabia, the world’s biggest oil exporter, told the Organization of Petroleum Exporting Countries (OPEC) that it kept pumping the most crude in three decades last month amid growing signs that the 12-nation group’s quest to maintain market share is working.

The kingdom produced 10.33 million barrels a day (MMbbl/d) in May, an increase of 25,000 barrels from April, according to data the country communicated to OPEC. The group supplied almost 31 million barrels a day collectively, the most in almost three years.

OPEC decided on June 5 to persist with a strategy of maintaining production, insisting suppliers outside the group should be the ones to curb a surplus. Oil stockpiles in developed economies are more than 100 million barrels above the five-year average for the time of year. U.S. production will peak this year and shale supply is starting to slow, Energy Department reports show.

“The current oversupply in the market is likely to ease over the coming quarters,” OPEC said in its monthly oil market report Wednesday. The group “expects non-OPEC supply to decline in the second half of 2015, compared to an increase in the first half.”

Brent crude futures for July settlement gained as much as $1.48, or 2.3%, to $66.36 a barrel on the London-based ICE Futures Europe exchange, the highest since May 22. The contract was at $66.21 as of 11:33 a.m. local time. Prices have risen 15% this year.

Slowing Growth

Supply from nations outside OPEC will expand by 680,000 bbl/d this year, “one third of the growth witnessed in 2014,” OPEC’s Vienna-based secretariat said in the report.

Total oil supply from the U.S., the world’s biggest consumer, will be an estimated 13.6 MMbbl/d in the second quarter this year before falling to 13.54 million by the end of the year, the report said. The number of rigs drilling for oil in the U.S. has fallen for 26 consecutive weeks, reducing the number of active machines by about 60% since October as the collapse in the price reduced profitability.

Crude production from shale formations such as North Dakota’s Bakken and Texas’s Eagle Ford will shrink 1.3% to 5.58 MMbbl/d this month, according to estimates from the U.S. Energy Information Administration (EIA). It’ll drop further in July to 5.49 million, the lowest level since January, the agency said.

U.S. Peak

Output in the U.S. will peak at a 43-year high in 2015 as producers work through a backlog of uncompleted wells before trailing off in the second half of the year. Production will increase to 9.43 MMbbl/d, the most since 1972, the EIA said Tuesday in its monthly Short-Term Energy Outlook. That’s 240,000 barrels higher than last month’s estimate.

Commercial oil stockpiles within the Organisation for Economic Co-operation and Development increased by 30.8 MMbbl to 2.776 billion barrels (Bbbl) in April, the highest since August 2010, according to OPEC forecasts. Commercial crude inventories rose for a fifth month in April to 1.395 billion barrels while product supplies were at 1.38 Bbbl, 16 million above the seasonal average.

OPEC pumped 30.975 MMbbl/d of crude in May, according to data from third parties compiled by the group’s analysts. The organization agreed last week to keep its output ceiling at 30 MMbbl/d and will meet again on Dec. 4. It has exceeded its target for the last 12 months, according to data compiled by Bloomberg.