Brent North Sea crude for delivery in June rose 94 cents to 85.17 dollars a barrel in midday London trade.
New York's main contract, light sweet crude for May, jumped 1.12 dollars to 82.57 dollars a barrel.
Oil prices had tumbled on Monday, closing down almost two dollars, amid concerns over fraud charges against Wall Street icon Goldman Sachs and the closure of European airports due to volcanic ash, traders said.
"The sell-off that happened in the markets due to the Goldman charges was quite overdone," said Clarence Chu, an oil trader with Hudson Capital Energy.
Chu said rebounding stock markets were pulling oil prices along with them. However, oil prices could see a drop this week as a supply backlog and slow demand weighed on the market, he told AFP.
Britain's financial regulator launched a formal investigation into Wall Street giant Goldman Sachs on Tuesday, in relation to US fraud charges that were filed against the bank last week.
In reaction, Goldman pledged to cooperate with the British probe following US fraud charges which it again dismissed as "unfounded".
Hours after the FSA announcement, the embattled US investment firm posted soaring first-quarter profits of 3.46 billion dollars (2.56 billion euros).
"Crude oil prices climbed higher (Tuesday) as the energy market seems to have already digested the concerns over Goldman Sachs," said Sucden Financial Research analyst Myrto Sokou.
Markets were also reacting to a pickup in jet fuel demand as planes increasingly took to the skies amid the volcanic ash cloud saga.
Oil was also winning support "from an increase in jet fuel demand and strong corporate earnings results from IBM and Citigroup that has spread a general optimism across the financial markets and boosted sentiment", said Sokou.
Elsewhere, China National Petroleum Corp. (CNPC), the country's top oil producer, aims to boost output at a giant Iraqi oilfield by 10 percent this year, a newspaper owned by the company said on Tuesday.
CNPC and Britain's BP in November signed a deal with Iraq to nearly triple production from the current one million barrels a day to 2.85 million barrels at the Rumaila field over the next six to seven years.
China has been aggressively securing overseas oil production contracts as it seek to meet soaring energy demand at home.
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