* U.S. stockpiles fall 4.143 million barrels in week- EIA
* OPEC, Russia expected to increase output
* OPEC and non-OPEC producers meet on June 22-23 in Vienna (New throughout, updates prices, market activity and comments; new byline, changes dateline, previously LONDON)
NEW YORK, June 13 (Reuters) - Oil prices edged higher on Wednesday, turning positive after U.S. government data showed a bigger weekly draw than expected in domestic crude inventories along with unexpected declines in gasoline and distillate stocks.
Earlier in the session, Brent and U.S. crude had retreated on concerns about rising production in the United States and expectations that OPEC and other producers could relax voluntary output cuts.
Brent crude was up 53 cents at $76.41 a barrel by 10:52 a.m. EDT (1552 GMT). U.S. light crude was up 10 cents at $66.46 a barrel.
U.S. crude stocks fell more than expected last week, while gasoline and distillate inventories dropped, the Energy Information Administration said on Wednesday. Crude inventories fell by 4.1 million barrels in the week to June 8, exceeding analysts' expectations for a decrease of 2.7 million barrels. U.S. estimated gasoline demand hit a record high of 9.88 million bpd in the week, the data said.
"The demand metrics here are amazing for crude oil and gasoline," said John Kilduff, a partner at Again Capital in New York. "Put the exports of crude on top of that, and it's just a really bullish report."
U.S. production rose to 10.9 million barrels a day in the week, but Kilduff said the market appeared able to absorb the increase. "It seems like we need almost every barrel of that to keep up with this refining demand."
With output in Russia rising back above 11 million bpd in June and Saudi production climbing to more than 10 million bpd, supplies from all three top producers are increasing.
The Organization of the Petroleum Exporting Countries and some non-OPEC producers, including Russia, started pumping less in 2017 to reduce a global crude glut. Prices have risen around 60 percent over the last year.
OPEC and other producers will meet on June 22-23 in Vienna to discuss future production.
"More oil from OPEC plus is the base case," said Bjarne Schieldrop, analyst at Swedish bank SEB.
"Saudi Arabia and Russia have already started to lift production," he said. "Unofficial sources have said Russia will propose to return production back to the October 2016 (level), i.e. removing the cap altogether over a period of three months."
Longer term, the market could tighten as demand increases if OPEC fails to cover supply shortfalls, the International Energy Agency said on Wednesday.
The IEA said it expects global oil demand to grow 1.4 million bpd this year, and in 2019, and will top 100 million bpd in the fourth quarter of 2018.
"The market will be finely balanced next year, and vulnerable to prices rising higher in the event of further disruption," the IEA said in its monthly report.
Fund manager Pierre Andurand at Andurand Capital is bullish.
"Prices will be above $150 in less than two years," he tweeted on Wednesday.
(Additional reporting by Henning Gloystein in Singapore and Christopher Johnson in London; Editing by David Gregorio and Dale Hudson)