Brent crude, the global benchmark, was down 65 cents, or 1.1 percent, at $59.56 a barrel by 9 a.m. ET (1400 GMT), after trading as high as $61.27.
Moscow has so far resisted joining any new production cuts and Falih did not say whether he had heard of any change in Russia's position.
To maximise revenue, the government pumped a record 4.69 million barrels a day in October.
Cost of January futures for Brent crude on London's ICE Futures exchange is $57,57 per barrel, or $1,19 (2.03 per cent) below level of closing of the previous session, reports the online edition of the Chronicle.info with reference to the Correspondent.
"Near-term oversupply has gutted Brent prices", US investment bank Jefferies said in a note on Friday, adding that there was "an increasing urgency to move crude into storage".
Since early November, oil prices dropped already at 23 percent.
Oil briefly plunged below $50 on Thursday amid fears of an emerging supply glut, before reversing course after Reuters, citing unnamed industry sources, reported that Russian Federation is considering cutting its oil output along with other members of the Oil and Petroleum Producing Countries (OPEC).
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Gastélum had requested assistance from the United Nations on Thursday amid what he described as a humanitarian crisis in Tijuana. What will be the fate of thousands at the border? "We're better off trying to negotiate that with the president".
Then came out a report by Reuters that Russian Federation has started to concede that it needs to join a new Saudi-led oil production cut, but is still bargaining with its key OPEC partner over how much, how fast, and for how long it would potentially reduce its oil output.
"Over the last week, we had bilateral consultations with Iraq, Libya, Russia, all that will lead us to reach a consensus".
Falih's challenge is to get other countries on board with output cuts to avert another crash in oil prices next year while disguising the kingdom's diminishing leverage in the oil market.
Saudi Arabia faces a familiar but uncomfortable choice: cut production to defend prices or allow prices to fall to protect market share.
Russian Federation is happy with the current oil price level of around $60 dollars per barrel, President Vladimir Putin said on Wednesday, despite a recent dramatic oil price slump on global oversupply worries.
Responding to a question on whether Nigeria would seek exemption for crude oil production cap at the OPEC meeting, he said that it was too early to determine, adding that Nigeria would continue to work with OPEC.
USA crude inventories have hit their highest in a year after a tenth consecutive weekly increase, and are now only 80 million barrels below March 2017's record 535 million barrels, according to the Energy Information Administration.