By early afternoon in Europe, benchmark crude for December delivery was up $2.75 at $94.02 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose $3.87, or 4.4 percent, to settle at $91.27 in New York on Monday.
In London, Brent crude was up 48 cents at $111.93 a barrel on the ICE Futures exchange.
Oil has jumped over 20 percent in three weeks amid growing investor optimism that European leaders will devise a plan to limit the damage from a possible default of Greek sovereign debt. Details of the plan are expected to be announced Wednesday.
"Although the eurozone debt issue remains quite murky, the market appears to be pricing in a viable resolution to this crisis," energy consultant Ritterbusch and Associates said in a report. "Wednesday's EU summit could still bring some bearish news if a comprehensive debt plan is not forthcoming."
While demand has seesawed over the past months, crude supplies are seen to be continuously thinner, said analysts at Barclays Capital in London.
"The oil market tightening that started in Europe and Japan has now spread to the U.S., with U.S. crude and oil product inventories having fallen at a rate of nearly 1 million barrels a day over the past month," Barclays said.
On Monday, crude futures moved into so-called backwardation — when the price of oil futures for upcoming contracts is lower than the current month contract — a trading pattern which usually reflects narrowing supplies.
Crude has also rebounded this month because of signs global economic growth may not slow as much as some investors had previously expected. China, which has led global commodity demand growth in recent years, said Monday manufacturing likely improved in October from September.
Last week, China said its economy grew 9.1 percent in the third quarter.
"We continue to grow more positive on the outlook for China's commodity import demand over the remainder of the year," Barclays Capital said in a report. "Improving evidence from the macroeconomic front for October are in line with our soft landing assumptions."
Oil prices were also sustained by threats to oil output from Hurricane Rina, a Category 2 storm expected to continue strengthening and become a major hurricane.
"Hurricane Rina is heading for the Yucatan Peninsula and could impact on crude production for Latin America's largest producer, Petroleos Mexicanos," said a report from Sucden Financial in London.
Investors will meanwhile be monitoring new figures on U.S. stockpiles of crude and refined products.
Data for the week ending Oct. 21 is expected to show a build of 200,000 barrels in crude oil stocks and a draw of 1.25 million barrels in gasoline stocks, according to a survey of analysts by Platts, the energy information arm of McGraw-Hill Cos.
The American Petroleum Institute will release its report on oil stocks later Tuesday, while the report from the Energy Department's Energy Information Administration — the market benchmark — will be out on Wednesday.
In other Nymex trading, heating oil was up 1.13 cents to $3.0655 per gallon and gasoline futures slid 0.94 cent to $2.6609 per gallon. Natural gas rose 2 cents at $3.624 per 1,000 cubic feet.
Alex Kennedy in Singapore contributed to this report.
Copyright 2011 The Associated Press.