But prices could also be hit by lower demand from China due to a trade war with the U.S.
Oil prices rose on Tuesday, with U.S. crude breaking through $70 a barrel, after the evacuation of two Gulf of Mexico oil platforms in preparation for a hurricane.
The Brent crude oil - the global benchmark for oil prices - was trading at $78.01 per barrel, however, closed trading at $79.38 per barrel.
Over the last two weeks, the two crude oil benchmarks have been steadily rising and show no sign of stopping.
Striking a balance between maximizing revenue and keeping a lid on prices in order not to stall demand, top crude exporter Saudi Arabia is managing its own supply with a goal to keep crude prices in a range between $70 and $80 per barrel, OPEC and industry sources told Reuters this week.
Anadarko Petroleum Corp APC.N said on Monday it had evacuated and shut production at two oil platforms in the northern Gulf of Mexico ahead of the approach of Gordon, which is expected to come ashore as a hurricane.
So far, the news is having a limited impact on Brent prices.
Japan's efforts to get a waiver from Washington that would allow it to continue importing oil from Iran appear to have been unsuccessful, according to Jiji Press, who adds that Japanese oil companies are now forced to prepare to suspend Iranian imports and investigate ways in which they can switch to other Middle East producers.
Iran's exports and oil production collapsed in 2012 after Barack Obama, then US president, led a global coalition to curb purchases to try to force the Persian country into restricting its nuclear program.
US light crude jumped $1.60 a barrel from Friday's close to a peak of $71.40, its highest since mid-July, before easing to around $70.65 by 1340 GMT. Investors anticipate less supply from Iran as U.S. sanctions on Tehran begin to bite.
The latest move also comes as major Japanese banks prepare to halt transactions related to Iran, which will make it hard for distributors to process payments even if they continue buying Iranian oil.
French bank BNP Paribas struck a similar tone, warning of "supply issues" for the rest of the year and into 2019.
The risk of declining Chinese demand for oil is worrying Middle East officials more than Iran's supply curbs as a result of USA sanctions.
The average retail price for a liter of regular has been above ¥150 since late May.