* Global markets drop as key Trump adviser departs
* Gary Cohn opposed Trump plans for steel, aluminum tariffs
* Soaring U.S. crude output, rising stocks also weigh
* U.S. crude output to climb to 11.17 mln bpd by Q4 -EIA (Updates with comment, refreshes prices; changes dateline from SINGAPORE)
LONDON, March 7 (Reuters) - Oil fell on Wednesday, in line with a broad decline on global financial markets, after a key advocate for free trade in the U.S. government resigned, feeding concern that Washington will go ahead with import tariffs and risk a trade war.
U.S. crude oil output is set to top 11 million barrels per day this year, making it the world's largest producer and threatening to offset the boost to prices from reduced supply from rivals within OPEC.
Gary Cohn, economic adviser to U.S. President Donald Trump, seen as a bulwark against protectionist forces within the government, said on Tuesday he was resigning, triggering a more than 1 percent fall in S&P 500 futures on Wednesday.
Crude oil followed suit. Brent futures were last down 85 cents on the day at $64.94 a barrel by 1005 GMT, while U.S. crude futures were down 69 cents at $61.91 a barrel.
Oil's correlation with the equity market has been positive, meaning the two tend to move in tandem, for at least a month, the longest such stretch in a year.
"With the announcement that Cohn was resigning, the S&P futures market dropped and oil went with it," Petromatrix strategist Olivier Jakob said.
"Today is going to be more about watching the S&P ... the correlation between the (index) and oil has been moving in synchronicity."
A voice for Wall Street in the White House, Cohn's resignation came after he lost a fight over Trump's plans for hefty steel and aluminum import tariffs.
Major powers, including the European Union and China, have warned that such tariffs could lead to retaliatory action and trigger a global trade war, which could bring to a halt economic growth and, by extension, oil consumption.
A rise in U.S. crude inventories also dented sentiment, even though stocks tend to rise at this time of year as refineries frequently close for maintenance.
Crude inventories rose by 5.661 million barrels last week to 426.880 million barrels, data from the American Petroleum Institute showed on Tuesday.
Official data by the U.S. Energy Information Administration (EIA) is due on Wednesday.
The EIA on Tuesday made its latest in a series of upward revisions for U.S. crude oil production <C-OUT-T-EIA>, which it now expects to rise by more than 120,000 barrels per day (bpd) to 11.17 million bpd by the fourth quarter of 2018.
That would take the United States past Russia to become the world's biggest oil producer. The United States already passed top exporter Saudi Arabia late last year.
For 2019, the EIA forecast a crude production increase of 570,000 bpd to 11.27 million bpd.
"Rising U.S. oil output coupled with a simultaneous upswing in domestic oil stockpiles has all the makings for a potent bearish cocktail," PVM Oil Associates strategist Stephen Brennock said.
(Additional reporting by Henning Gloystein in SINGAPORE; Editing by Adrian Croft)