New York's main contract, light sweet crude for delivery in September, jumped $1.31 to $97.01 a barrel.
Brent North Sea crude for September soared $2.25 to $118.99.
"What we are seeing is a relief rally in the oil markets... it is really due to the deal in the US regarding raising the debt ceiling," said Victor Shum, analyst at Purvin and Gertz energy consultants.
US president Barack Obama on Sunday announced an 11th-hour deal to avert a potentially catastrophic debt default for the United States, the world's richest country and biggest oil consumer.
The deal would raise the country's $14.3-trillion debt ceiling by about $2.4 trillion in two steps, while calling for roughly the same about in spending cuts over 10 years.
In the US Congress, leaders of the Democratic-held Senate and the Republican-led House of Representatives said they would present the framework to their rank-and-file on Monday ahead of final votes to approve the deal.
Attention will now be on whether lawmakers will be able to approve the deal before midnight Tuesday (0400 GMT Wednesday) to prevent the default.
Crude markets were depressed last week as the August 2 deadline for reaching a compromise debt deal loomed.
A default by the United States would send shudders through the global economy that could lead to another financial crisis, while likely reducing demand for crude oil.
Copyright AFP (Agence France-Presse), 2011