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* U.S. crude stockpiles drop, fuel inventories build -EIA

* Saudi Aramco cuts Feb supply to some Asian refiners -sources

* Europe extends lockdowns, with fingers crossed for vaccines

* China COVID-19 cases rise, millions more placed under lockdown

(New throughout; updates prices, market activity and comments to settlement)

By Laila Kearney

NEW YORK, Jan 13 (Reuters) - Oil prices fell on Wednesday, pulling back from recent gains, on concerns that rising global COVID-19 will hamper global fuel demand.

The market did find some support from weekly inventory figures that showed a drop in crude inventories and rising refinery production.

Brent crude prices settled at $56.06 a barrel, down 52 cents, or 0.9%. U.S. West Texas Intermediate (WTI) settled at $52.91 a barrel, falling 30 cents, or 0.6%.

Fuel demand has rebounded from last spring's shock falloff as the COVID-19 pandemic worsened, but governments continue to place restrictions on travel that will restrain energy demand for months, analysts said.

"While I see crude prices trading higher over the coming months, investors need to be mindful that the road to higher oil demand and prices will remain bumpy," UBS oil analyst Giovanni Staunovo said.

U.S. crude inventories were lower for a fifth straight week, dropping by 3.2 million barrels last week, exceeding analysts' expectations in a Reuters poll for a 2.3 million-barrel drop, as refiners increased crude runs, the Energy Information Administration said.

"The refiners are starting to see a better demand picture and that's being reflected not just what we're seeing in the United States but also overseas," said Phil Flynn, senior analyst at Price Futures Group in Chicago.

Governments across Europe announced tighter and longer coronavirus lockdowns on Wednesday due to a fast-spreading COVID variant first detected in Britain and as vaccinations are not expected to help much for another two to three months.

China recorded the biggest daily jump in coronavirus cases in more than five months, despite lockdowns, increased testing and other measures aimed at preventing another wave of infections.

Saudi Arabia cut supplies of crude for February loading for at least three Asian buyers, while meeting requirements of at least four others, several refinery and trade sources told Reuters.

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CHART: Brent oil may extend gains into $57.76-$58.17 range -

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(Additional reporting by Ahmad Ghaddar in London and Aaron Sheldrick in TOKYO; Editing by Marguerita Choy and David Gregorio)

((Laila.kearney@thomsonreuters.com; (917) 809-0054))