New York's main contract, West Texas Intermediate crude for delivery in April, added 82 cents to $107.16 a barrel.
Brent North Sea crude for April climbed $1.14 cents to $126.48 in London late afternoon trade.
On Tuesday, all eyes were on the US central bank's Federal Open Market Committee (FOMC), which is unlikely to budge from its easy-money stance, despite an improving American jobs market.
"Investors are awaiting the FOMC statement, due at 1815 GMT," said GFT analyst David Morrison.
"Not a lot is expected to come out of this, although investors are hoping that Fed chairman Bernanke may hint about further monetary stimulus when he speaks tomorrow.
"However this now seems less likely following Friday's better-than-expected US jobs report."
Hopes for higher crude consumption were lifted after data showed last week that the US economy added more than 200,000 jobs for the third straight month in February. The United States is the world's largest oil user.
Ahead of the Fed rate call, US data that US retail sales grew 1.1 per cent in February from January, their highest increase in five months.
Oil also won support from news that German investor confidence surged to the highest level for 21 months in March, amid optimism that Europe's top economy can shrug off the worst of the eurozone debt crisis.
The ZEW think tank's economic expectations index rose by 16.9 points in March to stand at plus 22.3 points, the highest level since June 2010, the organisation said in a statement on Tuesday.
Crude futures had fallen on Monday as investors fretted over the strength of worldwide demand following weak economic data in China, which is the world's biggest energy consuming nation.
"Prices reversed from yesterday's losses and corrected higher on Tuesday, supported by gains in the global equity markets and improved market sentiment after robust German economic data," said Sucden analyst Myrto Sokou.
"The ZEW ... showed encouraging signs about Germany's economic prospects and increased risk appetite," she added.
Elsewhere, traders kept a watch over tensions between major crude producer Iran and the West, analysts said.
Kuwaiti oil minister Hani Hussein said over the weekend that Iran's threat to close the Strait of Hormuz, a conduit for one fifth of the world's oil supplies, was a major cause for concern.