New York's main contract, West Texas Intermediate (WTI) light sweet crude for July delivery, rose 25 cents to $95.20 a barrel.
Brent North Sea crude for August gained four cents to $114.06.
"US crude futures rose in choppy trading, recouping some of the previous day's sharp losses after the International Energy Agency forecast a steep rise in demand," said a Phillip Futures report.
The IEA, in its monthly report Thursday, raised its global oil demand forecast for 2011 by 0.1 million barrels per day to 89.3 million barrels.
A predicted rise in demand hinted at a recovering US economy, which requires crude oil to fuel its industries, leading to higher prices.
New US claims for unemployment benefits fell to 414,000 in the week ending June 11, a decline of four% from the previous week, and US housing starts grew more than expected in May, rebounding 3.5% from April.
"However, the gain was limited due to the rising tension over a planned rescue of Greece, amid worries of wider fallout," the IEA report added.
Dealers have been rattled by the failure of eurozone finance ministers to reach an deal on a second bailout package aimed at averting a Greek debt default, which could plunge financial markets into crisis.
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