* OPEC says group's production up 336,000 bpd in May
* Saudi Arabia leads OPEC effort to tighten oil markets
* Not all OPEC members have complied with pledges to cut
* Rising U.S. output threatens to undermine Saudi efforts (Adds OPEC report, updates prices)
LONDON, June 13 (Reuters) - Oil prices edged down on Tuesday after OPEC reported an increase in its production for May despite a supply cut agreement and said the oil market was rebalancing more slowly than expected.
Benchmark Brent crude was 17 cents lower at $48.12 per barrel by 1236 GMT, reversing gains made earlier in the session when it edged up to $48.67. U.S. light crude was at $45.86 per barrel, down 22 cents.
Prices initially nudged higher after the world's top exporter Saudi Arabia outlined cuts to customers in July that included a reduction of 300,000 barrels per day (bpd) to Asia.
Riyadh is leading an effort by the Organization of the Petroleum Exporting Countries, Russia and other producers to cut output by almost 1.8 million bpd until March in a bid to curb oversupply and prop up prices.
But OPEC's monthly report showed output from the group rose by 336,000 bpd in May to 32.14 million bpd, led by a recovery in Nigeria and Libya which are exempt from supply cuts. The report said the market was rebalancing at a "slower pace".
"Crude oil is still struggling to rebound," said Olivier Jakob, strategist at Petromatrix, adding that OPEC's gradual approach to rebalancing was giving U.S. producers time to drill new wells that were undermining the impact of the group's cuts.
He said Saudi cuts had to continue beyond the northern hemisphere's summer months to have a significant impact
"They're making a lot of headlines about reducing supplies but that's also right in their seasonal pattern of lowering exports in July, August because of domestic needs," he said.
Trade data show OPEC shipments to customers averaged around 26 million bpd in the last six months of 2016 and are set to average around 25.3 million bpd in the first half of this year.
Meanwhile, U.S. drilling activity has continued apace <RIG-OL-USA-BHI>, driving up U.S. output <C-OUT-T-EIA> by more than 10 percent since mid-2016 to above 9.3 million bpd.
U.S. crude inventories remain stubbornly high. Traders will be watching figures on last week's U.S. stockpiles to be released later on Tuesday by industry group the American Petroleum Institute.
Traders said market intelligence firm Genscape had forecast a draw down of more than 1.8 million barrels at the Cushing, Oklahoma delivery point for U.S. crude futures.
"Where oil prices go will be determined by the flow of inventory data," said Greg McKenna, chief market strategist at Australian futures brokerage AxiTrader. (Additional reporting by Henning Gloystein in Singapore; Editing by Dale Hudson and Edmund Blair)