Opening the Strait of Hormuz is key to easing the pressure that the war in the Middle East has placed on energy prices and the global economy, the International Energy Agency (IEA) said.
The warning comes on the first full day of a new US blockade of the strait.
The IEA predicts that global oil supply will shrink this year as the war disrupts exports.
Demand will also shrink, the agency said, reversing its previous forecast for growth, as what it calls the biggest oil supply shock in history sends prices soaring.
Oil prices have risen sharply during the war, with the commodity occasionally changing hands at a near-record price of $150 per barrel, adding pressure on consumers and leading governments to introduce fuel-saving measures.
It has since fallen below $100.
The IEA said supply will fall by 1.5 million barrels a day this year, as attacks on energy assets in the Middle East and Iran's effective closure of the Strait of Hormuz hit production and exports.
The figure is equivalent to about 1.5% of global demand.
In March, the agency called the war in the Middle East the biggest oil supply disruption ever, and now it is warning of an even bigger drop in demand.
The war has “completely changed the global outlook for oil consumption,” the IEA said, predicting a drop of 80,000 barrels per day in demand growth this year. Last month, the agency had forecast a rise of 640,000 barrels per day.
"Resumption of flows through the Strait of Hormuz remains the most important variable in easing pressure on energy supplies, prices and the global economy," the agency said.
