Bullish bets by money managers on global benchmark Brent crude have declined for four weeks since mid-April, while front-month futures have jumped more than 10 percent over the past month.
By 1125 BST the price of Brent crude rose to $79.86 per barrel, around a three-and-a-half year high.
France's Total had on Wednesday warned it might abandon a multi-billion-dollar gas project in Iran if it could not secure a waiver from United States sanctions, casting further doubt on European-led efforts to salvage the nuclear deal. "We continued to receive support from concerns about supply from the Iranian nuclear accord, Venezuela.as well as the draw in crude", McGillian said.
"Global inventories are approaching long-run averages, suggesting that the coordinated OPEC/non-OPEC supply cuts have been successful", said Jack Allardyce, oil and gas research analyst at Cantor Fitzgerald.
While futures prices climb, physical crude markets are sagging under the weight of unsold barrels.
USA bank Morgan Stanley said it had raised its Brent price forecast to $90 per barrel by 2020 due to a steady increase in demand.
Senior market analyst Fiona Cincotta at City Index said that although the increased U.S. production is putting pressure on the oil prices, they are now overshadowed by the lack in production from both Iran and Venezuela.
On currency markets, the dollar has benefited from bets on higher US rates, keeping it around multi-month highs against its major peers.
Trump on 8 May announced the USA decision to withdraw from what he views as a "defective" pact, noting that the sanctions to be re-imposed are targeted at critical sectors of Iran's economy, such as energy, petrochemical and financial sectors.
On Wednesday, the U.S. Energy Information Administration reported that U.S. crude inventories dropped by 1.4 million barrels in the week to May 11, to 432.34 million barrels.
On the flip side, high oil prices would hurt consumption, the International Energy Agency warned on Wednesday as it lowered its global oil demand growth forecast for 2018 to 1.4 million bpd from 1.5 million bpd.
United States crude output has soared 27 per cent in the last two years to a record 10.72 million barrels per day, putting it within reach of top producer Russia's 11 million bpd.
The Organisation of the Petroleum Exporting Countries (Opec) has said that that it will not rethink its supply strategy even after oil reached $80 (£59) per barrel, labelling it a short-term spike rather than supply shortage.