Iranian representative Mohsen Mohebi told the court the USA sanctions are a clear breach of the 1955 treaty because they are "intended to damage, as severely as possible, Iran's economy".
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Iran's economy has slumped since US President Donald Trump ordered that the sanctions be reinstated in May.
Iran's currency the rial has lost around half its value since April.
In the latest blow, Iran's parliament impeached Economy Minister Masoud Karbasian on Sunday.
Why did the U.S. abandon the nuclear deal?
The Islamic Republic has threatened to block the waterway in the past in retaliation for the US pulling out of the Iran Nuclear Deal. He said they were needed to ensure Iran never builds a nuclear bomb and to address its continuing missile programme and support for terrorism.
The U.S. sanctions target Iran's vehicle industry, trade in gold and other precious metals, and purchases of U.S. dollars crucial to support its oil exports and other global trade.
A second wave of punitive measures are due to hit Iran in early November, targeting its vital energy sector including oil exports. The decision was met with resistance from key USA allies, including France and Germany, both of which attempted to talk Trump out of pulling out.
The flag carrier of the Netherlands, KLM, which is owned by the same parent company as Air France, had already announced they would discontinue flights to Tehran Sept. 23.
What is Iran arguing at the ICJ?
Hacen piñata de Thalía y ella la desea en su cumpleaños
Ahora la cantante se ha convertido en el centro de atención, luego que en México se creara una piñata en su honor. Un atuendo con flecos de color rosado que, también provocó una lluvia memes, según La República .
Iran demanded Monday that the UN's top court order the United States to suspend nuclear-linked sanctions against Tehran, but Washington vowed to "vigorously" fend off the legal challenge.
Iran filed a complaint against Washington in July, saying that by pulling out of the deal, the USA breached the Treaty of Amity, Economic Relations, and Consular Rights signed in 1955.
But on Thursday, two of the continent's biggest airlines announced they would back out of flights to Iran.
Trump said in May that he would pull the United States out of a 2015 agreement over Iran's nuclear program and would re-impose sanctions on Tehran.
"The US is publicly propagating a policy meant to damage as severely as possible Iran's economy and Iranian national companies, and therefore inevitably Iranian nationals", Mr Mohebi told the court on Monday.
"This policy is nothing but a naked economic aggression against my country", Mohebi told the court.
How has the U.S. responded?
"Turkey is a leading country among those we have good relations with", he told Iran's state television.
However, whether any decision will be implemented remains unclear, with both Iran and the U.S. in the past ignoring ICJ rulings against them.
Iran ignored a 1980 US suit at the ICJ over the seizure of American diplomats in Tehran, which the court found to be illegal.The ICJ ruled in 2003 that the US-Iran treaty was still valid even though it was signed before the Islamic revolution, but did not deem US actions against Iranian oil platforms nor Iranian attacks on American shipping to have violated the treaty.
The oral arguments, essentially a request by Iran for a provisional ruling, will last for four days, with a decision to follow within a month.