The price of oil changed little after a 5% fall over the last two days.
Benchmark crude for April delivery was down 12 cents to $92.72 a barrel in late morning trading on the New York Mercantile Exchange.
Brent crude, used to price oil that many US refineries use to make gasoline, rose 42 cents at $113.95 a barrel on the ICE Futures exchange in London.
Encouraging news about the global economy helped oil prices stabilise.
The European Commission said today that it expects the recession afflicting the economy of the 17 countries sharing the euro to bottom out during the first half of the year, with growth reaching an annual rate of 0.7% in the fourth quarter.
The EC expects growth in the eurozone to accelerate to 1.4% next year.
A stronger global economy is likely to mean more demand for oil and gas, which points to higher prices for fuel.
US stock markets rebounded from a recent slump on concerns about the fate of the Fed's stimulus program and looming budget cuts in Washington. Shortly before midday the major indexes were all higher.