U.S.-China trade talks this week also in focus.
Oil was close to its 2019 high of almost $67 a barrel on Tuesday, supported by OPEC-led supply cuts although gains were capped by concerns about slowing economic growth that could hit demand.
The supply curbs led by the Organization of the Petroleum Exporting Countries have helped crude oil prices to rise more than 20 percent this year. U.S. sanctions against OPEC members Iran and Venezuela have also tightened the market.
Brent crude slipped 21 cents to $66.29 a barrel by 1249 GMT, not far from the 2019 high of $66.83 reached on Monday. U.S. crude was up 44 cents at $56.03.
"The market is slowly regaining its bullish footing, subject to the perception of economic risks tied to U.S.-China trade talks," said Harry Tchilinguirian, global head of commodity markets strategy at BNP Paribas.
Demand-side worries remain the main drag on prices. HSBC Holdings warned on Tuesday that an economic slowdown in China and Britain would throw up further hurdles this year.
More talks between the United States and China to resolve their trade dispute will take place in Washington on Tuesday. Traders said they were cautious on taking large new positions before the outcome of the talks.
"If they falter, we run the risk of sell-offs like we had in December," Tchilinguirian said.
OPEC last week lowered its forecast for growth in world oil demand in 2019 to 1.24 million barrels per day and some analysts believe it could be weaker still.
"Given a continuously uncertain economic picture, our already relatively bearish outlook for 2019 of below 1 million bpd in global oil demand growth may be subject to further downwards revisions," analysts at JBC Energy said.
To stop a buildup of inventories that could weigh on prices, the group of OPEC and non-OPEC producers known as OPEC+ began a new supply cut of 1.2 million bpd on Jan. 1.
Top crude exporter Saudi Arabia has sharply reduced production and exports to ensure that the deal gets off to a strong start.
In keeping with that aim, the kingdom plans to reduce light crude oil supplies to Asian customers for March, two sources with knowledge of the matter said on Tuesday.
U.S. sanctions against exporters Iran and Venezuela have provided additional support to the market.
Venezuela is a major crude supplier to U.S. refineries. Iran's exports, while down steeply since the sanctions began in November, have actually risen in early 2019, according to tanker data and sources.
By Alex Lawler, Henning Gloystein and Colin Packham
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