West Texas Intermediate, the US marker, climbed 0.9 percent to $60.75, paring its losses after falling into a bear market last week.
OPEC's second-biggest producer Iraq has also indicated it may join in such a move.
His comments appeared to be a response to U.S. Special Representative for Iran Brian Hook, who said last week that Iranian vessels would lose access to worldwide insurance markets under the U.S. sanctions and so would be a risk to ports and canals which allowed them access.
That confounded a market that was anticipating stricter enforcement and a more significant reduction in Iranian exports.
Any official decision on global output cuts will be made at a key ministerial meeting for OPEC and non-OPEC producers in Vienna in early December, Falih said. He said the committee were reviewing the market and would draw up a plan to deal with the prospect of higher supply in 2019.
An official from group member Kuwait said on Monday major oil exporters over the weekend had "discussed a proposal for some kind of cut in (crude) supply next year", although the official did not provide any detail.
He said market sentiment had shifted from fears of shortages to worries about oversupply.
"With Iranian waivers coming in higher than anyone expected, Saudi Arabia is acting responsibly by reducing its production that it had earlier brought online to offset possible Iranian losses", said Amrita Sen, chief oil analyst at Energy Aspects Ltd, a consultant in London.
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Khalid al-Falih's comments follow a meeting in Abu Dhabi at the weekend, where the Organisation of Petroleum Exporting Countries (OPEC) and its allies started laying the groundwork to cut supply in 2019, reversing an nearly year-long expansion.
"A new strategy needs to be formed... whether it is a cut in production or something else, but it will not be an increase in production", he said.
"We have to study all the factors", he said.
Falih said the U.S. sanctions had removed less oil from the market than expected because of the waivers.
Dudley said the waivers had been unexpected, so the market had been readjusting.
Through large production cuts starting at the beginning of 2017, they managed to push up oil prices from below Dollars 30 a barrel to over USD 85 a barrel in October, strongly improving their revenues.
OPEC and Russian Federation are set to discuss oil production cuts again, less than a month after both Alexander Novak and Khalid al-Falih assured markets they will ramp up production to offset any supply losses after USA sanctions against Iran came into effect.
But producers eased output cuts in June after signs of a tighter market and higher prices, selling hundreds of thousands of extra barrels.