New York's main contract, light sweet crude for delivery in April edged up four cents to $105.47 a barrel.
Brent North Sea crude for April eased five cents to $124.92 in London midday deals.
"Market participants have a difficult task on their hands trying to balance significant risks to future supplies with a fairly downbeat demand growth outlook for the year," said Andrey Kryuchenkov, analyst at Russian financial group VTB Capital.
Later on Thursday, traders will digest a raft of economic data from the United States -- the world's largest oil-consuming nation -- that includes weekly jobless claims and producer prices.
The Federal Reserve Bank of New York will also publish its March Empire State Index, followed by the Philadelphia Fed Index for March.
Figures released Wednesday by the US Department of Energy (DoE) showed crude stocks were at a nine-month high after rising 2.5 million barrels last week. A rise in crude inventory is seen as a sign of weakening demand.
The DoE in the weekly report said total products supplied to the market over the past four weeks were down 5.4 percent from a year ago, with unseasonably warm weather continuing across much of the country.
Meanwhile, continued tensions between crude producer Iran and the West remain a key concern for traders.
Iran on Wednesday condemned what it said was the use of oil as a political tool against producers, referring to Western sanctions over its controversial nuclear programme.
Tehran has repeatedly said its nuclear activities are exclusively peaceful.
The International Energy Agency on Wednesday forecast (IEA) that Iranian oil exports would fall by 800,000 barrels per day after mid-2012.
The IEA said Iran's exports would decline to around one million bpd, while global demand for oil grows by 800,000 bpd to 89.9 million bpd.
The United States and the European Union have in the past four months ramped up economic sanctions on Iran in a bid to force it to suspend uranium enrichment, the most sensitive part of its nuclear programme.
Iran had warned in December that it would blockade the strategic Strait of Hormuz -- a key transit route for global oil supply -- if the West imposes further punitive measures.