By early afternoon in Europe, benchmark crude for October delivery had risen 34 cents to $97.51 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose 63 cents to $97.17 on the Nymex on Tuesday.
In London, Brent crude was up 63 cents at $116.03 on the ICE Futures exchange.
Oil prices have been caught between a push-pull of two events: the so-called shoulder period for fuel demand, and the start of a two-day meeting of the Federal Reserve's Open Market Committee.
Oil prices trend lower during shoulder periods — the time of year between summer, when gasoline is in high demand as Americans take to the road for vacation, and the winter when there is strong demand for heating oil.
But Fed action to help the U.S. economy might mean more demand for oil and other energy products — and higher fuel prices.
Another impetus for oil prices to rise came out of Germany on Wednesday, when the country's high court gave the government the go-ahead to participate in a European bailout fund.
While the decision contains certain conditions, it means the European Stability Mechanism can be signed off by the country's president so it can come into force by the end of the year.
"The German constitutional court's decision is supportive of strong oil prices but the impact is fairly neutral," said Caroline Bain, commodities analyst at the Economist Intelligence Unit in London. "If the court had ruled the bailout fund illegal then we would have expected a sharp fall in oil prices and in commodity prices more generally as the implication would have been for a return to heightened levels of financial market volatility and an exacerbation of the euro zone sovereign debt crisis."
Meanwhile, the International Energy Agency said the global pace of demand growth over the next 18 months would stay "relatively steady," with demand expected of rise by 800,000 barrels a day both this year and next. The Paris-based IEA forecast global oil demand of 89.8 million barrels a day in 2012 and of 90.6 million barrels in 2013, both up just marginally from its previous report released in August. The IEA said the adjustments reflected data revisions for 2011.
"This modest growth rate reflects the combined effects of sluggish global economic activity, historically elevated oil prices and global improvements in energy efficiency," the IEA said.
Risks to global growth include "bearish economic indicators from the U.S., the eurozone and now, increasingly, the engine of oil demand growth of the last decade — China," the IEA noted.
In other trading on Nymex, heating oil rose 1.33 cents to $3.199 per gallon. Wholesale gasoline gained 1.99 cents to $3.0634 per gallon and natural gas lost 0.4 cent to $2.988 per 1,000 cubic feet.
Pamela Sampson in Bangkok contributed to this report.
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