The United Nations Educational, Scientific and Cultural Organization (UNESCO) has said that both the United States and Iran must observe conventions obliging states to protect cultural sites after US President Donald Trump threatened to target Iran's cultural heritage.

At a meeting with the Iranian ambassador to the Paris-based organisation on Monday, Director-General Audrey Azoulay said provisions of the 1954 and 1972 conventions, ratified by both the US and Iran, should be observed.

The conventions ask the signatory states to not undertake any deliberate measures that might damage cultural and natural heritage on the territory of other states party to the conventions.

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Azoulay stressed "the universality of cultural and natural heritage as vectors of peace and dialogue between peoples", which the international community has a duty to protect and preserve for future generations.

Trump on Sunday stood by his threat to go after Iranian cultural sites, warning of a "major retaliation" if Iran strikes back for the killing of one of its top military commanders, Qassem Soleimani.

"They're allowed to use roadside bombs and blow up our people. And we're not allowed to touch their cultural site? It doesn't work that way," Trump said in a tweet without specifying the alleged attacks to which he was referring.

In response, Iran's Foreign Minister Mohammad Javad Zarif said such a move would be a "war crime".

The ancient city of Persepolis in Iran is a major draw for tourists [Delbars/Getty Images]

UNESCO was supported by the United Kingdom, whose Prime Minister Boris Johnson has been criticised for his silence over US-Iran tensions during his Christmas holiday.

James Slack, Johnson's official spokesman, reiterated UNESCO's comments, telling reporters during a briefing on Monday that "there are international conventions in place that prevent the destruction of cultural heritage".

Iran boasts 22 cultural sites and two natural sites on UNESCO's World Heritage list.

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Important Iranian cultural sites that are not on the UNESCO list include the Azadi Tower in the capital, Tehran, and the tomb of former Supreme Leader Ayatollah Ruhollah Khomeini.

Perhaps the most spectacular cultural site is the ancient Achaemenid capital of Persepolis in southwest Iran. Founded by Darius I in 518 BC, it is a major attraction for foreign tourists.

The US withdrew from UNESCO in 2019, along with Israel, over accusations of anti-Israel bias.

The Paris-based organisation had previously criticised Israel's occupation of East Jerusalem and granted full membership to Palestine in 2011.