Benchmark crude was up $1.61 to $104.85 per barrel at late afternoon Singapore time in electronic trading on the New York Mercantile Exchange. On Monday it traded at $105.44, the highest since May. The contract last settled on Friday when it rose 93 cents to $103.24 per barrel in New York.
Brent crude was up 15 cents at $120.20 per barrel in London.
U.S. markets were closed Monday for the Presidents Day holiday.
European Union officials agreed early Tuesday to hand Greece a second massive bailout to help save it from bankruptcy. Private bondholders will take a 53.5 percent loss on their holdings which, along with tough austerity measures, is hoped will lower Greece's debt level to about 120 percent of gross domestic product.
Crude has jumped from $96 earlier this month and $75 in October as signs of an improving U.S. economy bolstered investor confidence. However, analysts are concerned higher fuel costs could stifle consumer spending and undercut economic growth.
"A significant run-up in oil prices are an important contributor to an economic malaise," energy trader and consultant The Schork Group said in a report. "With the U.S. economy starting to show signs of life, high prices now just might kill this recovery in the cradle."
In other energy trading, heating oil added 2.1 cents to $3.20 per gallon and gasoline futures rose 2.5 cents to $3.21 per gallon. Natural gas slid 4.0 cents to $2.64 per 1,000 cubic feet.
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