* U.S. crude stocks fell more than expected last week - EIA
* OPEC, non-OPEC meetings over output deal set for July 1-2
* Graphic on U.S. stockpiles: https://tmsnrt.rs/2XkQF8e (Updates prices, market activity and comments)
NEW YORK, June 19 (Reuters) - Oil futures were little changed on Wednesday as price support from a larger-than-expected decline in U.S. crude inventories was countered by a slump in equities.
Brent crude futures shed 27 cents to $61.87 a barrel by 1:57 p.m. EDT (1757 GMT).
U.S. West Texas Intermediate crude futures lost 25 cents to $53.65 a barrel. On Tuesday, it had recorded its biggest daily rise since early January.
After swelling to near two-year highs, U.S. crude stocks fell 3.1 million barrels last week, compared with analysts' expectations for a draw of 1.1 million barrels, the Energy Information Administration (EIA) said.
Oil prices briefly turned positive after the EIA report.
"Definitely what we saw here is more of a normal report for this type of year," said Phil Flynn, analyst at Price Futures Group in Chicago. "Even with the bullish report, after the big run-up yesterday, the market is hesitant to drive a lot higher."
A pullback on Wall Street ahead of a U.S. Federal Reserve decision on interest rates also weighed on oil futures, which often follow equities.
"The crude oil market is correlating to that, and we'll probably correct accordingly whichever way the broader equities markets trade... after the Fed statement," said Bob Yawger, director of energy futures at Mizuho in New York.
The Federal Reserve concludes its latest two-day policy meeting on Wednesday and is expected to leave interest rates on hold but flag whether it plans to cut rates later this year. The Fed may nod to recent weaker-than-expected jobs numbers and softer inflation, and drop from its policy statement a pledge to be "patient" before changing rates.
Tensions remain high in the Middle East after last week's tanker attacks. Fears of a confrontation between Iran and the United States have mounted, with Washington blaming Tehran, which has denied any role.
Trump said he was prepared to take military action to stop Iran having a nuclear bomb but left open whether he would approve the use of force to protect Gulf oil supplies.
Oil markets have largely shrugged off a rocket attack on Wednesday on a site in southern Iraq used by foreign oil companies.
Members of the Organization of the Petroleum Exporting Countries have agreed to meet on July 1, followed by a meeting with non-OPEC allies on July 2, after weeks of wrangling over dates.
OPEC and its allies will discuss whether to extend a deal on cutting 1.2 million barrels per day of production that runs out this month.
(Additional reporting by Shadia Nasralla in London and Aaron Sheldrick in TOKYO Editing by Marguerita Choy and Alistair Bell)
