The price is still well below its peak of $147 a barrel
The price of oil has jumped by more than $16 to $120.92 a barrel, the biggest one-day gain on record.
There is uncertainty about how the government's financial bail-out plan will work, causing investors to switch to perceived safe havens such as oil.
Others believe that the US government's bail-out plan will help the economy, increasing demand for oil.
Concerns also persist about supply as production in the Gulf of Mexico is still affected by Hurricane Ike.
However, analysts said the US rescue package was key.
"[It] has changed sentiment in the oil market," said analyst Paul Harris from Bank of Ireland.
At one point during trading, the price of oil rose by more than $25. The volatility in the price has been exacerbated by the fact that the contract for the supply of oil in October expires on Monday.
The contract for oil to be delivered in November was not up as sharply. It rose by $6.62 to $109.37 in New York.
Last week oil traded as low as $91 a barrel. It had fallen from the peak of $147 a barrel it reached in July.