Iran's exports averaged about 209,000 bpd in May, Vortexa data shows, down sharply from 1.34 million bpd in April and nearly 1.9 million bpd in March.
IMF spokeswoman Julie Kozack said the fund expects global inventories to fall from their pre-war high of 8 billion barrels to about 7.5 billion barrels by July, which would be a five-year low.
Kazakhstan's oil transit via the northern Druzhba branch to Germany has, meanwhile, been halted since May due to what Russia said was a lack of "technical possibilities".
ANZ bank senior commodity strategist Daniel Hynes said any efforts to reopen the Strait of Hormuz face challenges as Iran has mined large portions of the vital waterway.
Exports to Caribbean terminals for storage fell to some 58,000 bpd from 187,000 bpd the previous month, a signal of larger demand from refiners for Venezuela's heavy crude grades and residual fuel.