But the militant group's opponents have warned that the move can invite US sanctions on a country that's already reeling under an economic crisis.
Leader of Hezbollah Hasan Nasrallah has said a tanker would set off from Iran "within hours" to bring desperately needed fuel supplies to Lebanon, in defiance of US sanctions.
Many questions remain about how the shipment would reach its stated destination, where acute and growing fuel shortages have forced hospitals, businesses and government offices shut amid a crippling economic crisis.
But the move, prohibited by US sanctions on Iran's oil industry, could drag Lebanon into the covert naval war between Tehran and Israel. Nasrallah dared Iran's foes to stop the shipment.
"The vessel, from the moment it sails in the coming hours until it enters (Mediterranean) waters, will be considered Lebanese territory," he said during a televised speech to mark the Shia Muslim commemoration of Ashura.
"To the Americans and Israelis, I say: it's Lebanese territory."
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More vessels to follow
He said a first ship would bring fuel for "hospitals, manufacturers of medicine and food, as well as bakeries and private generators."
He said more vessels would follow to address shortages that have ground Lebanon to a halt.
Neither the Iranian nor the Lebanese governments have confirmed the paramilitary organisation's claim.
Nasrallah did not specify where or how the shipment would reach Lebanon and be offloaded.
Lebanese energy expert Laury Haytayan said major questions hung over the shipment, including the amount to be delivered, who would pay, where the boat would dock and whether the details of the transaction had been disclosed to the Lebanese government.
"It is a possibility that these tankers will go to Syria and shipments will be refined there," Haytayan said.
"But this is all prohibited by sanctions, its not that easy, and since Hezbollah is doing it in public, there is a lot of danger on Lebanon, we are in danger of being sanctioned, or being attacked."
Former prime minister Saad Hariri warned Thursday that Nasrallah's remarks could be "dangerous."
"Iranian vessels will carry additional dangers and sanctions for the Lebanese," he said in a statement released by his office.
Nasrallah said his group does not aim to “defy anyone,” by arranging the fuel shipment from Iran, but added that “we cannot stand idle amid the humiliation of our people whether in front of bakeries, hospitals, gas stations and darkness at night.”
For weeks, Lebanese have been waiting in long lines at petrol stations to fill their car tanks. Diesel shortages amid severe power cuts have shut down thousands of private generators, leading to shortages of bread.
Some hospitals have warned that patients could die because of the diesel shortage.
The shortages are blamed on smuggling, hoarding and the cash-strapped government’s inability to secure deliveries of imported fuel.
Lebanon has for decades suffered electricity cuts, partly because of widespread corruption and mismanagement. The Mediterranean nation of 6 million — including 1 million Syrian refugees — is near bankruptcy.
The situation deteriorated dramatically last week after the central bank decided to end subsidies for fuel products.
The decision will likely lead to a hike in the prices of almost all commodities in Lebanon.