A rally from below $35 a barrel in March stalled last month on investor concern that a sluggish global economy may not recover fast enough to justify surging oil prices.
Traders will be eyeing the Labor Department's June unemployment report, due to be released later Thursday, for signs the economy and consumer demand could be improving.
The jobless rate hit a 25-year high of 9.4 percent in May, jumping from 8.9 percent the previous month.
Oil will likely trade between $65 a barrel and $75 in the July-September period, averaging $71 in the third quarter and $76 in the fourth quarter, Barclay Capital said in a report.
"We expect the upward momentum in many commodities to slow over the next few quarters, before fresh highs are reached when the cycle becomes expansive," Barclays said.
Prices were bolstered by a weekly crude inventory report from the Energy Department's Energy Information Administration which showed crude supplies fell more than some expected, losing 3.7 million barrels for the week ended June 26.
Supplies have dropped 15.8 million barrels during the last four weeks, a sign crude demand may be picking up.
In other Nymex trading, gasoline for August delivery was steady at $1.86 a gallon and heating oil held at $1.76. Natural gas for August delivery fell 1.3 cents to $3.78 per 1,000 cubic feet.
In London, Brent prices fell 9 cents to $68.70 a barrel on the ICE Futures exchange.
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