US crude stockpiles fell 8.6 million barrels last week, in contrast to expectations for an increase of 2.8 million barrels, government data showed.
The drawdown, which breaks five consecutive weeks of builds, was due to net crude imports slowing to a record low of 2.6 million barrels per day in the wake of declining OPEC production and US sanctions against Venezuela.
US crude futures settled at $56.94 a barrel, up $1.44, or 2.6 percent, the biggest daily percentage rise in nearly four weeks. Brent crude futures rose $1.18, or 1.8 percent, to end at $66.39 a barrel.
"Overall it's a very positive report with stronger demand, and I do think you're already seeing the impact from OPEC cuts," said Phil Flynn, analyst at Price Futures Group in Chicago.
Saudi Energy Minister Khalid al-Falih said the Organization of the Petroleum Exporting Countries and its partners were already "taking it easy" in response to a tweet from Trump on Monday, who told the group to "relax" on production cuts.
"The 25 countries are taking a very slow and measured approach" Falih said in Riyadh when asked to comment on Trump's tweet, CNBC reported. "Just as the second half of last year proved, we are interested in market stability first and foremost."
Oil prices have risen more than 20 percent so far this year after OPEC and non-member producer allies agreed to cut output for six months starting in January to avoid the build-up of a global surplus particularly as US crude production booms.
Falih said the group may need to extend its agreement to curb output until the end of 2019.
US crude output has set record highs for two straight weeks, hitting 12.1 million bpd last week, according to government data.
Also in Riyadh, OPEC Secretary General Mohammed Barkindo commented that managing world supply is difficult when two members - Iran and Venezuela - are under sanction from the United States.
Russian energy minister Alexander Novak also said this week the oil market was more or less stable and price volatility, which is unwelcome to both producers and consumers, was low.