UPDATE 6-Oil prices fall as U.S. stocks rise, output increase weighs

* Gary Cohn opposed Trump plans for steel, aluminium tariffs

* U.S. crude inventories rose by 2.4 mln barrels last week- EIA

* Soaring U.S. crude output, rising stocks also weigh (Updates market activity, prices, adds commentary; changes byline, dateline to NEW YORK, previously LONDON)

NEW YORK, March 7 (Reuters) - Oil prices fell on Wednesday after U.S. government data showed an increase in inventories and as financial markets slid amid concerns that Washington's plans for import tariffs could spark a trade war.

Rising U.S. crude output and climbing U.S. inventories have weighed on oil prices. The United States is set to become the world's biggest oil producer this year, threatening to offset supply cuts by OPEC, Russia and other producers.

West Texas Intermediate (WTI) crude futures fell 28 cents to $62.32 a barrel, a 0.5 percent loss, by 11:09 a.m. EST (1609 GMT).

Brent crude futures fell 29 cents to $65.50 a barrel, a 0.4 percent loss.

Prices pared some losses after data from the Energy Information Administration said U.S. crude inventories rose by 2.4 million barrels in the last week, compared with analysts' expectations for an increase of 2.7 million barrels.

"The smaller-than-expected inventory build led to swift short covering. However, I don't believe that this strength will be long-lived with rising U.S. production and a strengthening dollar," said Phillip Streible, senior market strategist at RJO Futures in Chicago.

Crude stocks at the Cushing, Oklahoma, delivery hub fell by 605,000 barrels, EIA said.

The resignation of Gary Cohn, economic adviser to U.S. President Donald Trump, who was seen as a bulwark against protectionist forces in the government, triggered a drop in Wall Street stocks and tempered investor risk appetite.

(Additional reporting by Amanda Cooper in London and Henning Gloystein in Singapore Editing by Susan Thomas)