Benchmark Brent crude was up 65 cents at $84.56 a barrel by 0850 GMT, having fallen as low as $82.66 on Monday. Brent hit a four-year high of $86.74 last week. US light crude was up 45 cents at $74.74.
"The oil market mood is exceptionally bullish, with fears growing that the US demands for an Iran oil embargo could cause a significant supply shortfall," said Julius Baer commodities research analyst Carsten Menke.
Iran's crude exports fell further in the first week of October, according to tanker data and an industry source, as buyers sought alternatives ahead of US sanctions that take effect on Nov. 4.
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 would increase crude output next month to 10.7 million bpd, 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".
Meanwhile, oil companies operating in the Gulf of Mexico shut down nearly 20 percent of oil production as Hurricane Michael moved towards eastern Gulf states including Florida.
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.
The International Monetary Fund on Tuesday cut its global economic growth forecasts for 2018 and 2019, saying trade tensions and rising import tariffs were taking a toll on commerce while emerging markets struggle with tighter financial conditions and capital outflows.