OPEC on June 13 said a long-awaited rebalancing of the oil market was under way at a "slower pace" and reported that its own output in May jumped due to gains in nations exempt from a pact to reduce supply.

In a monthly report, OPEC said its output rose by 336,000 barrels per day (bbl/d) in May to 32.14 million bbl/d led by a rebound in Nigeria and Libya, which were exempted from supply cuts because unrest and conflict had curbed their output.

OPEC said oil inventories in industrialized countries dropped in April and would extend a decline in the rest of the year, but a recovery in production in the U.S. was slowing efforts to get rid of excess supply.

"The rebalancing of the market is underway, but at a slower pace, given the changes in fundamentals since December, especially the shift in U.S. supply from an expected contraction to positive growth," OPEC said in the report.

Oil prices pared gains on June 13 after the release of the report to trade towards $48/bbl, below the $60 level that top OPEC producer Saudi Arabia would like to see and less than half the level of mid-2014.

Under the deal to support the market, OPEC is curbing output by about 1.2 million bbl/d and Russia and other non-OPEC producers are cutting by half as much. With the glut slow to shift, the producers agreed in May to prolong the accord until March 2018.

In the report, OPEC pointed to continued high compliance by its members with the supply deal and said oil stocks in OECD nations fell in April—although they are still 251 million barrels above the five-year average.

Supply from 11 OPEC members with production targets under the accord—all except Libya and Nigeria—averaged 29.729 million bbl/d last month, according to figures from secondary sources that OPEC uses to monitor output.

That means OPEC has again complied more than 100% with the plan, according to a Reuters calculation. OPEC did not publish a compliance number.

OPEC also lowered its estimate of oil supply growth from producers outside the group this year to 840,000 bbl/d from a previous forecast of 950,000 bbl/d, following the decision to extend the supply cut deal.

As a result, OPEC raised the expected demand for its crude this year by 100,000 bbl/d to 32.02 million bbl/d. That is still below its May output.

The OPEC production figures are for 13 members and do not yet include Equatorial Guinea, which joined last month.