Brent crude, which helps set the price for oil imported into the U.S., added 4 cents to $96.09 in London.
The Fed holds a two-day meeting that ends Wednesday, and in the past it has taken action to encourage Americans to spend and borrow. Many analysts think the struggles of the U.S. economy and Europe's debt crisis will compel the Fed to say or unveil something to try to boost confidence.
Any sign that the Fed is willing to take action could lift oil prices, which have fallen sharply during the past six weeks over fears that growth in the global economy will stall.
"The market is building on a little optimism that they'll do something," said Peter Donovan, an oil broker with Vantage Trading in New York.
Concerns about Iran's nuclear program also are pushing oil prices higher, Donovan said. Negotiations between six world powers and Iran — a major oil producer — appear to have accomplished little this week in Moscow. That increases the likelihood of a European oil embargo in July. And some analysts are concerned the matter will only be settled by an armed conflict in the Middle East.
Either action — an embargo or an attack on Iran — could cut into the world's supply of oil.
Even before its sudden drop, the price of oil had declined from a high this year of $109.77 on February 24.
U.S. gasoline prices continue to follow oil lower. On Tuesday, the national average fell below $3.50 per gallon (92 cents a liter) for the first time since Feb. 10, according to auto club AAA, Wright Express and Oil Price Information Service. The average price of gasoline in the U.S. has dropped 44 cents since peaking at $3.94 in early April. Along with the impact of lower crude prices, there's a greater supply of gasoline. Refineries tend to increase stockpiles of summer gasoline after Memorial Day.
In other futures trading, heating oil added 2.2 cents to $2.64 per gallon while wholesale gasoline fell by 1.2 cents to $2.649 per gallon. Natural gas lost 5.2 cents to $2.583 per 1,000 cubic feet.