By early afternoon in Europe, benchmark crude for May delivery was up 65 cents to $84.41 a barrel in electronic trading on the New York Mercantile Exchange. The contract climbed by $1.39 to settle at $83.76 on Wednesday.
Oil prices have jumped from $69 a barrel in early February on investor expectations that a gradual recovery in the U.S. economy this year will eventually boost crude consumption.
So far, however, demand remains sluggish. The Energy Information Administration said crude inventories rose by 2.9 million barrels last week, slightly more than analysts expected.
"A good portion of the buying seems to have come on 'good vibrations,' the vague sense that the economic recovery is gaining momentum, and that that should lead to heavier demand for oil products," consultancy Cameron Hanover said in a report.
Trading volume was low ahead of Friday's holiday, when global oil trading will be closed and when the week's most anticipated economic indicator, the U.S. unemployment figures, will be released.
Even if there is an increase in non-farm payrolls, "we need to keep in mind that the number of unemployed is so large that even some consecutive gains will not make a difference for this year's gasoline consumption but only maybe for the consumption of 2011 or more likely for 2012," said Olivier Jakob of Petromatrix in Switzerland.
Jakob also highlighted technical analysis showing that the Nymex contract soon could be on its way to $90 a barrel.
"With the break of the previous highs, the positive momentum is starting to be created in WTI and the next target will be $85 a barrel, then $85.70," Jakob said. "Above $85.70 there will be no solid resistance until $90 a barrel."
Others warned that the disconnect between weak demand and plentiful supplies cannot be ignored for long.
"For the past several weeks, every single day on the oil market seems like April Fools' Day to us, since even though fundamental conditions have still not improved and the oil market continues to be characterized by surpluses ... oil prices continue their upward trend," said a report on commodities from Commerzbank in Frankfurt.
"From a long-term perspective though, the physical demand and supply will be the decisive factor. Hence, we expect that reality will soon catch up with the oil market and that the oil prices will come under significant pressure. For the time being, however, the price momentum remains positive."
Crude traders often look to equity markets as a measure of overall investor sentiment, and all major Asian and European stock indexes rose Thursday.
In other Nymex trading in May contracts, heating oil rose 1.69 cents to $2.1959 a gallon, and gasoline gained 1.29 cents to $2.3201 a gallon. Natural gas advanced 1.7 cents to $3.886 per 1,000 cubic feet.
In London, Brent crude was up 61 cents at $83.26 on the ICE futures exchange.