Further price support is provided by supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC) to tighten the market.
"You have the sanctions on Venezuela, on top of the reduced supply from Saudi Arabia", Olivier Jakob, oil analyst at Petromatrix, said as cited by Reuters. "There's no sign of overhang in the crude oil markets".
International Brent crude oil futures were at $62.72 a barrel, also up 21 cents or 0.4 percent, after closing down 0.4 percent in the previous session.
They closed down 1.3 percent on Monday, after earlier touching their highest since November 21 at $55.75 a barrel.
US West Texas Intermediate (WTI) crude futures were at $53.82 per barrel at 0607 GMT, down 19 cents, or 0.4 per cent, from their last settlement.
Meanwhile, average weekly United States crude oil production remained at the record 11.9 million barrels per day (bpd) it reached in late 2018. All in all, many analysts expect the heightened oil price volatility we have been witnessing for a few months now to remain throughout 2019.
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Saudi Arabia's exports to the U.S. finished 2018 at just 530,000 barrels per day, a massive drop from the 940,000 overage over the last five years. "That said, if the other OPEC countries fail to offset this outage, the oil market could quickly become undersupplied, driving the price up".
At 447.2 million barrels, US crude oil inventories are about 6 percent above the five year average for this time of year, the EIA reported.
Following a USA decision to impose sanctions on Venezuela's oil industry last week, Guaido and the Trump administration have sought to appoint a new board of directors for Citgo. US crude output stayed at a record-high 11.9 million barrels a day.
"Supply fundamentals have increasingly been turning supportive in recent weeks, but against this the market still worries about the yet-to-be-realised - if at all - impact on demand from weaker macroeconomic fundamentals", said Ole Hansen, head of commodity strategy at Saxo Bank. Oil fell on Tuesday after a survey showed euro zone business expansion almost stalled in January.
US President Donald Trump said in his State of the Union address that a trade deal was possible with China.
Trump has vowed to increase US tariffs on $200 billion worth of Chinese imports to 25 percent from 10 percent now if the two sides can not reach a deal by March 1.