Earlier this month US President Donald Trump´s controversially pulled Washington out of an global deal with Iran that placed limits on its nuclear programme in return for easing economic sanctions.
The US West Texas Intermediate crude rose by 41 cents at $71.90 after also hitting its highest since November 2014, at $72.30 per barrel.
Brent crude for July delivery traded down about 0.5% at $78.02 a barrel in London.
"We are back to the situation where we were before the 2016 agreement and in the meantime Iran has grown its exports by 1 million barrels a day", Pouyanne said.
U.S. President Donald Trump's decision this month to withdraw from an global nuclear deal with Iran and revive sanctions that could limit crude exports from OPEC's third-largest producer has boosted oil prices.
"The geopolitical noise and escalation fears are here to stay". "We continued to receive support from concerns about supply from the Iranian nuclear accord, Venezuela.as well as the draw in crude", McGillian said.
In addition, fresh USA crude data which emerged on Wednesday piqued concerns by revealing a larger than expected drop in the country's overall supplies ahead of the high-demand summer driving season.
Oil hits new multi-year high above $80/bbl on Iran concerns
ANALYST TAKE: Connor Campbell, financial analyst at Spreadex, said USA stocks have struggled to claw back Tuesday's trade war-inspired losses "with little on the horizon in the rest of the week, beyond an unforeseen update on the state of play between the US and China, to spark a recovery".
"While the sharp rise in U.S. production and rig count has raised questions on the sustainability of inventory draws through 2018, we believe that inventories will continue to draw as we enter the summer driving season in 2018", they said.
OPEC crude oil production in April decreased by 130,000 barrels a day to 31.65 million barrels, largely due to further deterioration in Venezuelan production and lower output from Africa.
"The recent jump in oil prices will take its toll", said the agency.
"The API inventory data in the USA fits with. a topping pattern - or at least a decent pause - for oil prices at the moment", said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
Analysts pointed out that the oil market remained relatively calm as there was no new catalyst on Thursday, but uncertainties remain due to USA sanctions on Iran.
Investors were also monitoring the economic crisis in Venezuela which has seen a steep fall in the country's oil production, adding to supply concerns.
WTI light sweet was down 10 cents at USD71.37 a barrel at last check, off its early highs but still near a recent 4-year peak.