Brent crude futures were up 84 cents, or 1.28 percent, to settle at $66.58 a barrel.

US West Texas Intermediate (WTI) crude futures rose 72 cents, or 1.28 percent, to settle at $56.79 a barrel, a 1.28 percent.

Falih told Reuters on Sunday it would be too early to change a production curb pact agreed by the Organization of the Petroleum Exporting Countries and allies including Russia before the group's meeting in June.

"The Saudis continue to take a proactive approach to get supply and demand in better balance," said Andrew Lipow, president of Lipow Oil Associates in Houston.

Oil markets have been supported this year by the ongoing supply cuts by the group called OPEC+, which has pledged to cut 1.2 million barrels per day (bpd) in crude supply since the start of the year to prop up prices.

The group will meet on April 17-18, with another gathering scheduled for June 25-26, to discuss supply policy.

OPEC is expected to review global oil demand and supply balance as the group maintains production cuts during the April meeting, a senior Gulf oil official said on Monday.

"We want to see commercial stocks down," the official said on the sidelines of IHS Markit's CERAWeek energy conference.

The official added that global crude and oil products stocks should fall back to a five-year average, a target the group had set to drain a global oil glut.

In addition, a Saudi official said the country planned to cut crude oil exports in April to below 7 million barrels per day.

Prices were also buoyed by US energy services firm Baker Hughes' latest weekly report showing the number of rigs drilling for new oil production in the United States fell by nine to 834.

But the Paris-based International Energy Agency said in an outlook on Monday that crude output in the United States will rise nearly 2.8 million bpd to 13.7 million bpd in 2024 from about 11 million bpd in 2018.

US oil production could become less responsive to crude prices as major oil companies expand operations in the nation's shale fields, IEA officials said at the CERAWeek energy conference in Houston on Monday.

Markets were pressured after US employment data on Friday raised concerns that an economic slowdown in Asia and Europe was spilling into the United States.

"Brent prices have struggled to push firmly above $65/bbl in part because a strong US dollar remains a major headwind for commodity prices. In addition, global GDP growth has been soft and oil demand has yet to pick up seasonally," Bank of America Merrill Lynch said in a report.

But citing the OPEC+ cuts and low global stocks, the bank predicted prices for Brent would reach $70 a barrel this year.