Front-month Brent crude futures, the global benchmark for oil prices, were at $62.71 at 0630 GMT, 42 cents, or 0.7%, above Friday's close.
China's crude oil imports slipped to around 40.23 million tonnes in May, from an all-time high of 43.73 million tonnes in April, customs data showed, due to a drop in Iranian imports caused by USA sanctions and refinery maintenance.
Trade tensions between the United States and China, the world's two biggest oil consumers, also weighed on prices.
U.S. West Texas Intermediate (WTI) crude futures were at $54.32 per barrel, 33 cents, or 0.6%.
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Several OPEC sources said the most likely scenario now was keeping the production cut steady in the second half of 2019.
"Over the past week or so, our economists have revised down their GDP growth outlook for the US, China, India and Brazil", Barclays bank said on Monday in a note about the economy and its impact on oil demand.
With the next OPEC meeting few weeks away, the market is eyeing whether the world's major oil producers would prolong their supply cuts.
President Vladimir Putin said last week that Russian Federation and the Organization of the Petroleum Exporting Countries (OPEC) disagreed over what constituted a fair price for oil, but that they would take a joint decision at the policy meeting.
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Supporting oil prices Tuesday was optimism Opec+, which includes most Opec members along with a number of non-Opec producers led by Russian Federation, would extend its 1.2 Mmbpd crude production cut, in effect since January 1, but slated to end June 30.
"Oil prices have struggled to retain bullish gains as traders stay cautious over heightened geopolitical risks and persistent weakness in the global economic backdrop", said Benjamin Lu, commodities analyst at Phillips Future in Singapore.
Al Falih, who was in Moscow on Monday, said he and Russian Energy Minister Alexander Novak may have final opportunity to discuss the deal this month at a G20 meeting in Japan before OPEC and its allies hold a policy meeting in Vienna.
OPEC is due to meet on June 25 after talks with its allies led by Russian Federation on June 26, although sources have told Reuters that Russian Federation has suggested a date change to July 3 to 4.
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