Futures were steady in New York after adding 0.1% on Monday.
American crude stockpiles fell by 1.7 million barrels last week, according to a Bloomberg survey before Energy Information Administration data on Friday.
US industry figures are due later Tuesday.
Iraq pared output by 110,000 barrels a day in December, according to Petro-Logistics SA.
Oil has rallied about 10% this month after the US and China made a breakthrough on trade and the Organization of Petroleum Exporting Countries and its partners including Russia agreed to deepen output cuts.
American crude inventories are shrinking even as the nation pumps near record levels and shale explorers boost drilling.
“Prices are rising but the market is monitoring data on US oil production and inventories,” Jun Inoue, senior economist at Mizuho Research Institute, said by email.
Crude has been bolstered by the Opec+ decision to cut production further and the progress of trade talks between the US and China, he said.
West Texas Intermediate for February delivery fell 1 cent to US$60.51 a barrel as of 12.28pm Singapore time on the New York Mercantile Exchange.
The contract added 8 cents to close at US$60.52 on Monday.
Brent for February settlement rose 5 cents to US$66.44 a barrel on the ICE Futures Europe Exchange.
The contract gained 25 cents to close at US$66.39 on Monday.
The global benchmark traded at a US$5.94 premium to WTI.
US crude stockpiles are set to drop for a second week, extending a decline from the highest level in four months.
Separately, Saudi Arabia’s pressure on fellow Opec nations to do a better job of cutting output is prompting Iraq to reduce supplies to honour some of its outstanding commitments, according to data from Petro-Logistics and Genscape.
Oil prices are likely to remain in check during 2020 as Opec+ production cuts are offset by higher output from other countries and a mixed outlook for demand, according to analysts.
Mizuho’s Inoue estimates WTI will range from US$55 to US$65 a barrel next year, while Goldman Sachs Group Inc increased its forecast for Brent to US$63 from US$60.