New York's main contract, light sweet crude for July delivery, gained 35 cents to $100.94 a barrel and Brent North Sea crude for July delivery was up 58 cents at $115.26.
"The euro has hit a three-week high (Tuesday) on optimism and hope that Greece can get a second bailout," said Ong Yi Ling, a commodity analyst for Phillip Futures in Singapore.
"This optimism caused the euro to rebound and the dollar to weaken, leading to higher prices in Asian trade," she added.
The euro fetched $1.4371 in early Asian trade, up from $1.4264 late Monday.
A weaker dollar makes dollar-priced commodities such as crude futures cheaper for investors holding other currencies.
Traders are looking to US markets for leads when they reopen Tuesday. Markets in the US, the world's biggest oil consumer, were closed Monday for Memorial Day holiday.
Copyright AFP (Agence France-Presse), 2011