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* Brent, WTI ease on demand worries over trade war
* Iran tensions put a floor under losses
* Interactive graphic on U.S. output and storage: https://tmsnrt.rs/2Ino66i (Adds comment, updates prices)
TOKYO, July 9 (Reuters) - Oil prices dipped on Tuesday on demand concerns following the latest signs the U.S.-China trade war is dragging on the global economy, although the potential for conflicts in the Middle East offered support.
Brent crude futures were down 14 cents, or 0.2%, at $63.97 a barrel by 0524 GMT. They fell 12 cents on Monday.
U.S. West Texas Intermediate crude futures were down 20 cents, or 0.4%, at $57.46 a barrel. They rose 15 cents in the previous session.
Oil prices are being pressured by worries about demand as the U.S.-China trade war, heading into its second year, dampens prospects for global economic growth, which affects oil demand. The countries are the world's two largest oil consumers.
Japan's core machinery orders fell by the most in eight months, data showed on Monday, in a sign the global trade tensions are taking a toll on corporate investment.
Japanese government figures on Tuesday also showed that real wages in the country fell for a fifth straight month. The country is the world's fourth-largest user of crude.
"The weaker global economic outlook is keeping oil prices under downward pressure, but tensions in the Middle East are enhancing awareness to possible supply risk and should keep a floor under oil in the medium term," said Stephen Innes, managing partner at Vanguard Markets in Bangkok.
Hedge funds sold more Brent futures and options last week as concerns about the global economy trumped the decision by the Organization of the Petroleum Exporting Countries (OPEC) and its allies to extend output cuts.
Iran on Monday threatened to restart deactivated centrifuges and step up its enrichment of uranium to 20% in a move that further threatens the 2015 nuclear agreement that Washington abandoned last year.
Washington has imposed sanctions that eliminate benefits Iran was meant to receive in return for agreeing to curbs on its nuclear program under the 2015 deal with world powers.
The confrontation has brought the United States and Iran close to conflict. Last month, U.S. President Donald Trump called off air strikes at the last minute in retaliation for Iran shooting down a U.S. drone over the Gulf.
Meanwhile, Goldman Sachs said growth in U.S. shale production was likely to outpace that of global demand at least through 2020, limiting gains in oil prices despite output curbs led by OPEC.
Industry and government data for release later on Tuesday and on Wednesday is expected to show that U.S. crude stockpiles fell for a fourth consecutive week, dropping 3.6 million barrels, according to a preliminary Reuters poll.
(Reporting by Aaron Sheldrick; Editing by Christian Schmollinger and Richard Pullin)