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"It may impact oil companies' appetite for investment, so (Iran) might not cut production but it might go some way towards dampening their ability to maintain, let alone increase, production," Hansen, a senior manager at Saxo Bank, added.
Brent crude futures were up 41 cents at $65.36 a barrel by 1415 GMT, off an earlier low of $64.35, while U.S. West Texas Intermediate (WTI) crude futures were up 34 cents at $61.70 a barrel.
Both crude benchmarks dropped by around 1 percent on Monday after the U.S. Energy Information Administration said output from the shale basin would hit a new record high in April.
U.S. crude inventories are expected to show an increase later in the day when the American Petroleum Institute reports its weekly findings.
U.S. crude production from major shale formations is expected to rise by 131,000 bpd in April from the previous month to a record 6.95 million bpd, the U.S. Energy Information Administration (EIA) said in a monthly report on Monday.
That expected increase would top the 105,000 bpd climb in March from the previous month, to what was then expected to be a record high of 6.82 million bpd, the EIA said.