WTI futures were down 3.3% so far for the week, marking the largest weekly loss in 10 weeks, while Brent was down 3.2% on the week, its largest weekly loss in seven.
Comments by Trump on Wednesday, which signaled that a resolution to the US trade dispute with China might be near, helped limit losses.
Rouhani also urged the USA to "cease this policy of maximum pressure" in favour of "dialogue, and logic and reason".
Tensions between Iran and the West have risen since Trump withdrew the USA from Iran's 2015 nuclear deal with several world powers, saying the agreement was woefully inadequate.
"We've really been following headline to headline", said Phil Flynn, an analyst with Price Futures Group in Chicago.
The recent Energy Information Administration's report showing a surprise buildup in USA crude stockpile last week and reports saying Saudi Arabia has restored its oil production much faster than expected weighed on oil prices.
The 14 September attacks on the two plants caused heavy damage to the two plants and crude production had to be halved by shutting down 5.7 million bpd of production.
Saudi Crown Prince Mohammed bin Salman hosted Iraq's Prime Minister Adel Abdel Mahdi for talks on Wednesday targeted on assaults on the dominion's oil infrastructure, which Washington has blamed on Iran.
"It will depend on the global economy".
They should have started a bull run, but supply shocks that have rocked the oil industry this year have failed to deliver a sustained rise in crude prices. After pulling out of the landmark accord, the United States also reimposed crippling sanctions on Iran's oil and banking sectors in what it calls a "maximum pressure" campaign.
US President Donald Trump (picture) on Wednesday signalled that a resolution to the dispute with China might be near, which could eventually boost fuel demand.
The initial token deployment "will augment the kingdom's air and missile defense of critical military and civilian infrastructure", and will add to "an already significant presence of USA forces in the region", he said.
Moving on, numbers from the Baker Hughes' weekly US Oil Rig Count, prior 719, might occupy the data-line whereas trade/political news could keep offering the background music.