Benchmark Brent crude ended Tuesday's session up $1.09, or 1.3 percent, at $85 a barrel, having fallen as low as $82.66 on Monday. Brent hit a four-year high of $86.74 last week.
U.S. West Texas Intermediate crude settled 67 cents, or nearly 1 percent, higher at $74.96. WTI hit $76.90, a nearly four-year high, last week.
"The oil market mood is exceptionally bullish, with fears growing that the U.S. demands for an Iran oil embargo could cause a significant supply shortfall," said Julius Baer commodities research analyst Carsten Menke.
Iran exported 1.1 million barrels per day (bpd) of crude in that seven-day period, Refinitiv Eikon data showed. An industry source who also tracks exports said October shipments were so far below 1 million bpd.
That is down from at least 2.5 million bpd in April, before President Donald Trump in May withdrew the United States from a 2015 nuclear deal with Iran and reimposed sanctions. The figure also marks a further fall from 1.6 million bpd in September.
Saudi Arabia, the biggest producer in the Organization of the Petroleum Exporting Countries, said last week it has increased crude output in October to 10.7 million bpd, near a record.
"Iranian barrels are declining fast, and Saudi Arabia's promise to balance will face a reality check in a month's time," JP Morgan analysts said in a note.
Iranian Oil Minister Bijan Zanganeh on Monday called a Saudi claim that the kingdom could replace Iran's crude exports "nonsense."
If forecasts prove accurate, the hurricane would largely miss major oil-producing assets in the Gulf, analysts said, but a change of track could widen the impact.
Companies turned off about 324,200 barrels of oil and 284 million cubic feet of natural gas by midday on Monday. An update on shut-ins Tuesday is likely to show greater impact as more producers took action later in the day.
Coastal and onshore energy businesses also started preparations for what is expected to become a Category 3 storm packing winds of at least 111 miles per hour (178 km per hour).