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Front-month US WTI crude futures rose over a dollar to a session high of $56.85 a barrel before dipping back to $56.11 early on Tuesday. Brent crude was up 46 cents at $60.57 a barrel.

Analysts said expectations of firm US economic data later in the day had pushed prices higher.

"The focus of today would likely come from US durable orders and US GDP figures. Durable goods orders depict a strong manufacturing sector which implies a higher industrial use of crude oil," said Singapore-based Phillip Futures in a report on Tuesday.

"With the US economy picking up, we expect the figures to be favorable."

Tuesday's price rises followed a volatile session on Monday, when Brent prices first jumped to almost $63 a barrel on the back of strong international market performances before sliding back to not much over $60 after Saudi Arabia's powerful oil minister said Opec would not cut production at any price.

"Brent could drop below $60 per barrel over the next six months, and WTI could fall to $50, as global oil inventories build sharply from here," Bank of America Merrill Lynch said in a research note.

"The faster the oil price drop, the larger the damage to the global oil industry. Oil could rebound sharply by the end of 2015," it added.

While the reluctance of producer club Opec to cut output has pulled down prices, oil could receive some support from falling activity in the US, where many drillers are struggling to make money at current price levels. "US oil drilling has begun to fall sharply. We expect this fall to continue apace throughout Q1, unless there is an unexpectedly early move up in oil prices," Standard Chartered said in a report.