* China's May refining activity dips away from April strength
* U.S. crude output hits record 10.9 million bpd
* OPEC, Russia also expected to gradually increase production (Adds China refining data, updates prices)
SINGAPORE, June 14 (Reuters) - Oil prices eased on Thursday, dragged down by rising output and a decline in China's refining activity, although strong fuel consumption in the United States and a drop in its crude inventories provided the market with some support.
Brent crude futures were at $76.55 per barrel at 0445 GMT, down 19 cents, or 0.25 percent, from their last close.
U.S. West Texas Intermediate (WTI) crude futures were at $66.62 a barrel, down 2 cents from their last settlement.
China on Thursday reported a drop in its refinery activity, from 12.06 million barrels per day (bpd) in April to 11.93 million bpd in May, although year-on-year runs were still up by 8.2 percent.
Also weighing on prices was another rise in U.S. oil production <C-OUT-T-EIA>, which hit a weekly record of 10.9 million bpd last week, according to the Energy Information Administration (EIA) on Wednesday.
U.S. crude output has risen by almost 30 percent in the last two years, and it is now close to top global producer Russia, which produced 11.1 million bpd overall in the first two weeks of June.
But the rising output came amid strong demand, which traders said prevented crude prices from falling further.
U.S. consumption of gasoline in the United States rose to an historic high of 9.88 million bpd last week, according to the EIA.
U.S. crude inventories <C-STK-T-EIA> fell by 4.1 million barrels in the week to June 8, to 432.4 million barrels.
Still, U.S. output is now above that of top exporter Saudi Arabia, which currently churns out slightly above 10 million bpd.
WORLD CUP MEETING
The surge in American output puts pressure on other producers, who are losing market share.
Russian and Saudi production has been held back voluntarily since 2017, when the Organization of the Petroleum Exporting Countries (OPEC), together with some non-OPEC producers including Russia, started supply cuts aimed at propping up prices.
With Brent prices up by around 180 percent from their 2016 lows and demand strong, OPEC and Russia may soon end their voluntary supply cuts.
OPEC, together with Russia, will officially meet in Vienna on June 22 to discuss its production policy,
U.S. bank Morgan Stanley said OPEC and its partners had "largely achieved their stated objective of rebalancing the oil market."
With demand for oil strong, Morgan Stanley said the group's "production is likely to creep higher."
OPEC's de-facto leader Saudi Arabia and Russia will also have the chance to talk before the Vienna meeting.
Russia and Saudi Arabia are set to open the football world cup, which kicks off in Russia on Thursday.
"The two producers' ministers plan to discuss the issue during tomorrow's World Cup game between the two countries," ANZ bank said.
(Reporting by Henning Gloystein; editing by Richard Pullin)