New York's main contract, West Texas Intermediate (WTI) light sweet crude for July delivery, rose 48 cents to $95.29 a barrel.
Brent North Sea crude for delivery in August gained 99 cents to $114.00 on its first trading day.
Bargain-hunting traders were buying up crude after its overnight dip, said Victor Shum, a Singapore-based analyst at Purvin and Gertz international energy consultancy.
"Traders view this as a buying opportunity after oil prices tumbled," he told AFP.
WTI crude prices had dived more than $4.50 in late US trade yesterday, sinking below $95 as investors fretted about fresh signs of weakness in the US economy and tensions in Greece sent the dollar jumping.
Data from the US released Wednesday showed manufacturing conditions in New York falling into negative territory for the first time since November 2010 as inflation rates soared to their highest level in more than two-and-a-half years.
Markets had also been rattled by the failure of eurozone finance ministers to reach an accord in Brussels Tuesday on a second bailout package aimed at averting a Greek debt default, sending the dollar sharply higher against the euro.