In London, Brent prices fell $1.41 to $58.80 a barrel on the ICE Futures exchange.
Oil prices have jumped above $60 a barrel this month from below $35 in March as investors anticipate an eventual recovery of the U.S. economy from a severe recession.
"The market is looking six months down the line," said Mark Pervan, senior commodity strategist with ANZ Bank in Melbourne. "Right now, the actual physical demand for crude remains very weak."
Traders will be looking at fresh evidence of the health of the U.S. economy when a consumer confidence index for May and reports on sales of existing and new homes last month are released this week.
Some investors are optimistic that gasoline prices that are a third lower than last year will boost demand during the U.S. summer vacation period, which runs from late May to early September.
"The U.S. driving season could surprise on the upside," Pervan said. "We could see a pretty strong demand period over the next month or two."
Traders and analysts were also keeping an eye on this Thursday's OPEC meeting in Vienna.
"The general consensus is that the group will leave current production targets in place," said JBC Energy in Vienna, adding that "a surprise cut may be on the cards."
Saudi Arabia's oil minister, however, said that the 12-member Organization of the Petroleum Exporting Countries is unlikely to cut output at its upcoming meeting.
In comments published Tuesday in the pan-Arab daily Al-Hayat, Ali al-Naimi also voiced concerns about global crude stockpiles, which are being kept at high levels by weak demand linked to the economic downturn.
Sabotage of a major crude pipeline in Nigeria helped support oil prices. The rebel group called the Movement for the Emancipation of the Niger Delta said it had destroyed pipes run by Chevron Corp. Monday as the military carries out its largest operation in years against militants.
Chevron confirmed an incident on its pipeline network and said it caused them to shut down operations totaling 100,000 barrels per day.
In other Nymex trading, gasoline for June delivery fell 4.48 cents to $1.7960 a gallon and heating oil dropped 5.09 cents to $1.4871 a gallon. Natural gas for June delivery slid 8 cents to $3.435 per 1,000 cubic feet.
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Associated Press writer Alex Kennedy in Singapore contributed to this report.
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