Benchmark West Texas Intermediate crude for February delivery rose 79 cents to close at US$92.59 a barrel on the New York Mercantile Exchange.
Brent crude, used to set prices for international varieties of crude used by many U.S. refineries, fell 86 cents to close at US$106.39 in London.
"The overall outlook for oil pricing has taken on an increasingly mixed look with the two main crude benchmarks responding to differing influences," energy analyst Jim Ritterbusch wrote in a report Tuesday.
The U.S. stock market rose 0.9 per cent, in part on retail sales that were stronger than expected. That could mean demand for fuel, which has been rising in the U.S. in recent months, may continue to grow.
Still, the price of U.S. oil has fallen steadily since the beginning of the year because supplies of crude and fuels appear ample enough to offset rising demand. Tuesday marked only the third gain of the month for U.S. crude.
Global supplies could still be on the rise, which could mean lower prices for international crude, analysts say. Libyan crude production is beginning to ramp up after protests and unrest cut production late last year.
North Sea output is due to increase with the restart of the Buzzard oil field.
An agreement Sunday between Iran and six world powers may enable Iran's oil industry, whose exports were severely limited by sanctions over its nuclear program, to sell more crude after the deal takes effect Jan. 20.
Later this week, investors will be monitoring new information on U.S. stockpiles of crude and refined products. Data for the week ended Jan. 10 is expected to show a draw of 1.6 million barrels in crude oil stockpiles. It is also expected to show an increase of 1.7 million barrels in gasoline stockpiles, according to a survey of analysts by Platts, the energy information arm of McGraw-Hill Cos.
The expected draw would be the seventh consecutive decline in U.S. crude oil inventories. The report from the U.S. Energy Department's Energy Information Administration — the market benchmark — will come out Wednesday.
In other energy futures trading in New York: wholesale gasoline was down 1.2 cents to close at US$2.622 a U.S. gallon (3.79 litres), heating oil rose 0.3 cents to close at US$2.936 a gallon and natural gas rose 9.5 cents to close at US$4.369 per 1,000 cubic feet.
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