UPDATE 5-Oil prices fall on U.S. crude build, euro zone data

* U.S. crude stockpiles rose by 4.3 mln barrels last week - API

Euro zone economy at risk of contracting in fourth quarter - PMI

* IMF cuts euro zone growth forecasts

* Iran starts injecting uranium gas into centrifuges (Updates prices, IMF's remarks, Novak's remark, adds graphics)

By Bozorgmehr Sharafedin and Jane Chung

LONDON/SEOUL, Nov 6 (Reuters) - Oil prices fell on Wednesday, pulled down by a larger-than-expected build in U.S. crude stocks and weak euro zone economic figures, after gaining for three sessions on expectations of an easing in U.S.-China trade tensions.

Brent crude was down 57 cents at $62.39 a barrel by 1331 GMT.

West Texas Intermediate crude moved 38 cents lower to $56.85 per barrel.

Russian Energy Minister Alexander Novak said the current oil price of more than $60 per barrel shows that markets are stable.

The prices were pressured as U.S. crude inventories rose by 4.3 million barrels in the week ended Nov. 1 to 440.5 million barrels, the American Petroleum Institute said on Tuesday. That was nearly triple analysts' forecast for an increase of 1.5 million barrels.

Official data from the U.S. government's Energy Information Administration is due later on Wednesday.

"Oil prices are slightly under pressure following API's larger-than-expected crude build on Tuesday. Market participants will closely monitor if the build is confirmed by the EIA later today, considering that last week API had a crude draw and the EIA a crude build," said Giovanni Staunovo, oil analyst for UBS.

The United States and China, the world's two biggest oil consumers, are working to narrow their differences enough to sign a "phase one" trade deal as early as this month to resolve a trade war that has slowed global growth.

The International Monetary Fund (IMF) said euro zone economic growth is set to slow more than expected as the bloc's manufacturing crisis could spill over to the larger services sector under global trade tensions.

Data on Wednesday showed Germany's services sector barely grew in October, while euro zone business activity expanded slightly faster than expected last month, but remained close to stagnation.

Adding to Middle East tensions, Iran started to inject uranium gas into centrifuges at an underground nuclear facility, further distancing itself from a 2015 nuclear deal between Tehran and world powers.

Last year, U.S. President Donald Trump exited the deal and renewed sanctions on Tehran, slashing its oil sales by more than 80%.

"Alongside the continued rolling back of its nuclear commitments, the OPEC nation may be tempted to cause further supply disruptions in the Middle East in a bid to drive up prices," PVM analyst Stephen Brennock said.

"Accordingly, conditions are ripe for tensions in the region to escalate and for the geopolitical risk premium to strike back with a vengeance."

(Reporting by Bozorgmehr Sharafedin in London and Jane Chung in Seoul; Editing by Dale Hudson and Louise Heavens)