Brent crude oil futures were up 10 cents at $71.52 a barrel by 0907 GMT, while U.S. crude futures gained 9 cents to $66.31 a barrel.
U.S. President Donald Trump has threatened to pull out of a nuclear deal between Iran and six major powers by May 12 unless Congress and European allies help "fix" it with a follow-up agreement.
Oil markets have been well supported this year, with Brent up around 16 percent from its 2018 low in February, due to healthy demand and supply cuts led by the Organization of the Petroleum Exporting Countries.
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