European benchmark Brent North Sea crude for delivery in March jumped $1.40 to trade at $56.15 a barrel in late afternoon deals in London.
West Texas Intermediate (WTI) for March won $1.53 to $51.10 a barrel compared with Monday's close.
Earlier on Tuesday, prices earlier hit their highest levels since early January, with Brent and WTI striking $57.23 and $51.56 respectively.
"The strong rally continues in the oil market as both Brent and WTI front month futures extended gains and climbed higher... supported by increased appetite amid hopes of a rebound of the global oil demand in the first half of 2015," said Myrto Sokou, analyst at Sucden brokers.
Crude futures also rose Monday after US firms cut drilling activity,
The weekly Baker Hughes rig count, a barometer of drilling activity in the United States, showed a record drop of 94 oil rigs to 1,223 for the week to January 30.
The cuts in drilling rigs came on the heels of announcements by Chevron, ConocoPhillips and Royal Dutch Shell that they will slash budgets in 2015.
On Tuesday, Britain's BP and BG Group said they too would take the axe to costs.
Some analysts doubt the current oil price rebound will be sustained as supplies still far outweigh demand.
"Oil ... has enjoyed the combination of weakening supply and rising demand fundamentals to maintain its surge for another day," added Chris Beauchamp, market analyst at trading firm IG.
"Oversupply does not disappear overnight, however, and the jury is still out on whether this bounce (in prices) has much further to run."
Oil prices have lost as much as 60 percent of their value since June last year when the commodity was sitting at more than $100 a barrel.
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