On Thursday, data from the Energy Information Administration showed that US crude inventories USOILC=ECI unexpectedly fell 1.6 million barrels last week.
U.S. West Texas Intermediate crude for April delivery was up 20 cents, or 0.3 percent, at $63.75 a barrel by 0342 GMT after rising 3 percent last week.
That means rather than the US becoming awash in oil once again as shale drillers ramp up production, much of the additional barrels could be shipped overseas.
The deal to cut oil output by 1.8 million barrels a day (bpd) was adopted last winter by OPEC, Russia and nine other global producers. Equities markets weakened on Wednesday, while the USA dollar.DXY hit a one-month high.
Oil prices extended gains to hit their highest level in almost three weeks on Monday, supported by comments from Saudi Arabia that it would continue to curb exports in line with the OPEC-led effort to cut global supplies.
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For the record, al-Falih foresees a monitoring mechanism not too far removed from the one that now governs the OPEC cuts: "What we want is an evergreen framework that brings producers from OPEC and non-OPEC (countries) together in a market monitoring fashion that allows us to take quick decisions".
Most of this liquidation seems to be attributable to profit-taking after the big rally in oil prices over the last seven months.
"The standoff "shale versus sheikh" continues to frame the oil market, with the former again gaining the upper hand", said Norbert Ruecker, head of macro and commodity research at Julius Baer.
"Global oil fundamentals have been improving ever since OPEC and its allies agreed for production cuts, and the demand story is still supporting prices".
U.S. oil is also increasingly being exported, including to the world's biggest and fastest growing markets in Asia, eating away at OPEC and Russian market share. "Investors are now keeping a close watch on the US inventory number as growth has been rather slower than expectations". The US Henry Hub front month futures price remained close to the lowest level reached since August 2016.
Crude inventories rose by 933,000 barrels in the week to 421.2 million, compared with analyst expectations for an increase of 2.1 million barrels. "We see more downside for oil". Crude slipped after an industry report was said to show an increase in United States crude stockpiles.