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New York's main futures contract, light sweet crude for July delivery, rose 56 cents to USD 66.87 a barrel.
Brent North Sea crude for delivery in July advanced 54 cents to USD 66.06.
"Oil is heading up this morning. It's actually moving in sync with stock markets in Asia.... What's really supporting oil is primarily investors buying commodities as the US dollar weakens," said Victor Shum, an analyst with Purvin and Gertz energy consultancy in Singapore.
A weak US currency makes dollar-priced oil cheaper for holders of stronger currencies and in turn, tends to stimulate demand and push prices higher.
The US dollar is losing allure among investors amid growing signs of a recovery in the global economy as they seek higher yields from other foreign currencies, analysts said.
Investors usually favour the US dollar because of its safe haven status in times of economic uncertainty despite the low returns compared with other units.
However, Shum cautioned that the rally was "very fragile" as global energy demand remained weak.
"The reality is that there is a big contradiction confronting oil markets today. Fundamentals are very weak but oil prices have increased by 50 per cent since last December amid a glut of oil," he said.