Shipping data showed that traffic through the Strait of Hormuz dropped to six vessels on Monday, compared with a 10-day average of about 11 vessels.
In a note on Monday, Barclays analysts said that crude oil and refined product net exports through the Strait of Hormuz averaged 3 million barrels per day (bpd) in the week ending August 7, down from 4.4 million bpd the previous week.
Before the Iran conflict began in late February, about a fifth of global daily oil and liquefied natural gas supplies passed through the Strait of Hormuz.
A cargo ship was attacked on Tuesday by Yemen's Iran-aligned Houthis in the Bab el-Mandeb Strait, killing three crew members, said two Yemeni coast guard sources and two military officials in the government.
"The chokehold risk around both the Strait of Hormuz and the Bab el-Mandeb remains highly significant. Even intermittent restrictions or the threat of further incidents keep insurance costs elevated and force longer shipping routes ... hence energy flows look likely to stay constrained near term," said Tim Waterer, chief market analyst at KCM Trade.
Elsewhere, the Ukrainian military said on Tuesday that it had attacked an oil refinery in Orsk, the second-largest city in Russia's Orenburg region and an important industrial hub.