A potential withdrawal in May by US President Donald Trump from a 2015 nuclear deal between world powers and Iran would reimpose sanctions on the producer and curb its exports.
Meanwhile, Opec is trimming output even after concluding it has cleared 97 per cent of the surplus that has weighed on prices.
Oil prices have surged to levels last seen in 2014 as everything from the conflict in Syria to tensions between Saudi Arabia and Iran-backed rebels in Yemen stoked concerns over supply disruptions. French President Emmanuel Macron made a joint announcement with the office of Iranian President Hassan Rouhani that the two leaders would work together on preserving the deal.
"Prices have rallied as Opec and its allies including Russian Federation have eroded global inventories and as geopolitical risks surrounding the United States and the Middle East have increased this month".
US West Texas Intermediate (WTI) futures were last down 9 cents on the day at $68.01 a barrel, having recovered from an intraday low of $67.17.
Brent crude oil futures were down 40 cents at $73.46 United States a barrel mid-morning Wednesday, slipping further from the November 2014 high of $75.47 reached on Tuesday. Prices are up 5.2 per cent for the month. The global benchmark crude traded at a $6.43 premium to June WTI.
Trade was quiet in Asia as many markets including China, India and Singapore were closed for public holidays.
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Brent crude, the global benchmark traded in London, closed at a level not see since late 2014.
Weekly data on Tuesday that showed a rise in U.S. crude inventories also subdued the oil price somewhat.
"They want to try and work out a deal that could be independent of any kind of Trump walk-away", said Bob Yawger, director of futures at Mizuho Securities USA Inc.in NY.
If the USA does reimpose sanctions, that would be bullish for oil prices, analysts say, coinciding with a rapid decline in OPEC production largely due to declines in Angola and Venezuela, which is in the midst of an economic and social crisis.
A rise in USA government borrowing costs to their highest since 2013 this week has tempered some investor appetite for risk, but analysts said they believed Brent crude may have another attempt at marking new 2018 highs above $75 a barrel. The rig fleet has expanded throughout the entire month of April, adding a total 28 units.
US crude inventories likely rose by 1.3 million barrels last week, while gasoline and distillate stockpiles fell, a preliminary Reuters poll showed on Monday ahead of data by the Industry group the American Petroleum Institute later in the day.