Iran has appealed to the UN's highest court against a US Supreme Court ruling that $2 billion in frozen Iranian assets must be paid to American victims of terror attacks blamed on Tehran, the tribunal said Wednesday.

In its filing to the International Court of Justice (ICJ) based in The Hague on Tuesday, Tehran argues that "Iran and Iranian state-owned companies are entitled to immunity from the jurisdiction of the US courts", the tribunal said in a statement.

The US Supreme Court ruled in April that Iran must hand over nearly $2 billion (1.7 billion euros) in frozen assets to survivors and relatives of those killed in attacks blamed on the Islamic republic.

These included the 1983 bombing of a US Marine barracks in Beirut and the 1996 Khobar Towers bombing in Saudi Arabia.

The decision affects more than 1,000 Americans.

Tehran, which signed a landmark nuclear deal last year with world powers leading to the unblocking of other frozen funds, has reacted angrily to the Supreme Court ruling.

Iranian President Hassan Rouhani announced late Wednesday that "Iran has officially lodged a complaint with the international court and we will pursue our case until we get a result."

"The American courts have illegally decided that these funds must be given to Americans and the families of victims killed in Lebanon," he said, quoted by Iranian media.

"It remains unclear what these Americans were doing in Lebanon, and how this affair concerns Iran."

In its filing to the ICJ, the Islamic Republic argues that the legal proceedings underway in the US breach the terms of a 1955 bilateral treaty of amity, economic relations, and consular rights signed with the United States.

It further calls for the United States "to make full reparations to Iran for the violation of its international legal obligations in an amount to be determined by the court at a subsequent stage of the proceedings."

- Sanctions relief 'too slow' -

After more than a decade as an international pariah, Iran took a step back onto the world stage in July 2015 when after years of tough and protracted negotiations it struck a landmark deal in Vienna to rein in its suspect nuclear programme.

In return for the scaling down of its nuclear activities, painful UN and Western sanctions were lifted on the Islamic republic, including on its lifeblood oil exports.

Iran however has complained that major powers have been slow to implement their side of the bargain, with badly needed foreign investment into the country proving slower than hoped.

The United States has also maintained its sanctions targeting Tehran's alleged sponsorship of armed movements in the Middle East, such as Hezbollah in Lebanon, and its ballistic missile programme.

Iranian Foreign Minister Mohammad Javad Zarif on May 21 called on Washington to take "more serious and concrete actions" to alleviate the situation.

In Tuesday's filing, Iran says that because the US has maintained its designation of the country as a major state sponsor of terrorism its assets including the Central Bank, also known as the Bank Markazi, have been "subjected to enforcement proceedings in the United States" even if they should benefit from immunity under the 1955 treaty.

To date US courts have "awarded total damages of over US$ 56 billion... against Iran in respect of its alleged involvement in various terrorist acts mainly outside the USA," Iran says, according to the ICJ statement.

The UN court, which recently marked its 70th anniversary, will now have to decide whether it has jurisdiction to rule in the case.

Iran's supreme leader Ayatollah Ali Khamenei has meanwhile warned candidates in the US presidential election against questioning the Islamic republic's nuclear deal.

"We do not violate the nuclear accord... candidates in the American presidential election are threatening to tear up the nuclear deal. If they do so, we will burn it," he told visiting dignitaries, his website said Tuesday.