Benchmark West Texas Intermediate crude for March delivery was up 76 cents to close at US$97.19 a barrel on the New York Mercantile Exchange, reversing much of oil's loss Monday.
Brent crude, a benchmark for international oil used by many U.S. refineries, was down 26 cents to close at US$105.78 in London.
The U.S. oil price rose along with the stock market, which regained some ground Tuesday after a drop of 2.3 per cent Monday.
Stock markets around the world have been slammed by currency problems in several emerging market countries, the U.S. Federal Reserve's decision to shrink its stimulus program and a slowdown in the Chinese economy.
Tuesday's modest recovery in the U.S. stock market and a report by real estate data firm CoreLogic that showed a strong rise in U.S. home prices in December eased some fears that U.S. demand for fuel would fall.
So far this year, economic concerns have weighed less on oil prices than on stock prices, analysts say. That's partly because a bitterly cold winter in the U.S. has increased demand for heating oil, which is keeping demand for crude — and global prices — strong compared with stock prices.
Forecasts for further cold across much of the U.S. sent natural gas for March delivery soaring 47 cents, or 9.6 per cent, to close at US$5.375 per 1,000 cubic feet. That's the highest price for natural gas since February 2010, other than a short price spike last week in a thinly-traded expiring futures contract.
In other energy futures trading in New York: wholesale gasoline was down 0.4 cents to close at US$2.603 a U.S. gallon (3.79 litres) and heating oil was down 2.5 cents to close at US$2.983 a gallon.
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