Benchmark West Texas Intermediate crude for August delivery rose 18 cents to close at US$95.50 a barrel on the New York Mercantile Exchange.
That was in the middle of its range for June, when prices have swung between $91.26 and $99.21 a barrel.
The U.S. Energy Department's weekly report on energy supplies had little impact.
Crude supplies remained at 394.1 million barrels, 1.8 per cent above year-ago levels, the Energy Information Administration said.
Brent crude, which is used to set prices for oil used by many U.S. refineries to make gasoline, rose 40 cents to finish at US$101.66 a barrel.
In other energy futures trading on the Nymex, natural gas rose six cents to end at US$3.71 per 1,000 cubic feet, heating oil was flat at US$2.85 a U.S. gallon (3.79 litres) and wholesale gasoline dropped one cent to US$2.73 a gallon.
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