New York's main contract, West Texas Intermediate crude for delivery in September, jumped $1.65 to $87.03 a barrel.
Brent North Sea crude for September gained $1.20 to $109.23 a barrel in late London deals.
Global stock markets were firmer on Monday, steadying after the upheaval of last week. The euro rallied against the dollar after the European Central Bank said it bought 22 billion euros of government bonds last week to help ease the pressure on Italy and Spain, pushing down their borrowing costs.
A weaker dollar makes oil priced in the US currency cheaper for holders of other currencies, pushing up demand for the commodity.
Crude futures had fallen earlier on Monday amid a downbeat outlook for energy demand owing to the spectre of another global recession.
Victor Shum, an analyst with Purvin and Gertz energy consultants, told AFP that he expects the oil market to stay volatile.
"I expect that the market will continue to be rocky and volatile because there's still concern about a potential return of the global economy to a recession," he said.
Crude oil meanwhile rose on Monday after last week riding the same rollercoaster as global stock markets.
"Looking back at Friday where Brent made no gains despite the positive developments in equity markets indicates that there is a careful attitude in the oil market," said Bjarne Schieldrop, a commodities analyst at Swedish bank SEB.
World Bank chief Robert Zoellick said in Australia on Sunday that investors had lost confidence in the economic leadership of several key countries and warned that global markets were consequently in a "new danger zone".
Zoellick said a convergence of events in the United States and Europe had rattled investors in countries already struggling to cap sovereign debt issues and unemployment.
"And what we've seen is that confidence is a fragile element of how the market economy works," he said.
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