New York's main contract, light sweet crude for February delivery, rose nine cents to 91.47 dollars per barrel.
Brent North Sea crude for February was up five cents at 94.80 dollars.
The two contracts had closed 2010 at a two-year high, buoyed by hopes that improved US economic momentum will bolster global growth and translate into higher oil demand, analysts said.
"A stronger US dollar means that the US economy is gaining momentum, which increases the future demand in oil," said Ong Yi Ling, an investment analyst from Phillip Futures in Singapore.
In early Asian trade, the dollar traded at 81.33 yen compared with 81.28 yen on Friday while the euro was quoted at 1.3289 against the dollar, down slightly from 1.3381.
The United States is the world's biggest oil consuming nation and the recent cold winter spell in its northeast region also boosted crude prices.