The Cyrus cylinder, made around 530BC. Its lettering decrees that everyone should be free to practise their own religion. Photograph: British Museum

Britain's troubled relations with Iran have become further strained by a row about an ancient Persian artefact described as the world's first charter of human rights.

The British Museum is refusing to honour an agreement to lend the Cyrus cylinder to Iran because of the political turmoil that has gripped the country since the violently disputed re-election of Mahmoud Ahmadinejad in June.

The Iranian authorities have responded by threatening to sever links with the British Museum if it delays lending the 2,500-year-old cylinder, which was ordered by the Persian king Cyrus the Great to enshrine religious toleration.

Persian scholars claim the museum is right to be wary of lending the cylinder because of attempts by antisemitic historians in Iran to attack Cyrus's reputation as the father of the Iranian nation.

On a visit to Tehran's Museum of Iran this week, Hamid Baqaie, vice president of Iran's Cultural Heritage, Handicrafts and Tourism Organisation, said: "The British Museum implies the post-election political situation in Iran as its main excuse not to loan the cylinder to Iran's National Museum."

He added: "If the British Museum continues to make excuses for not loaning the artefact to the National Museum, we will, unfortunately, cease any co-operation with them, including archaeological expeditions and research."

The director of the British Museum, Neil MacGregor, agreed to lend the 23cm-long (9in) clay cylinder in return for several Iranian treasures. Those pieces were the focus of a critically acclaimed exhibition about the era of Shah Abbas that sought to break down the perception of Iran as a hostile nation.

The cylinder was made around 530BC on the orders of Cyrus the Great after he invaded Babylon and freed its people from tyranny. It is known as the first charter of human rights as its cuneiform lettering decrees that everyone should be free to practise their own culture and religion. Iran's sizeable Jewish population trace their presence in Iran to this moment.

Hannah Boulton, head of press and public relations at British Museum, tried to play down the row. "When lending any material you have to check that is an appropriate moment," she said.

"We are committed to lending the Cyrus cylinder to Iran. We hope to be able to honour that commitment, we can't say when that will be. At the moment we are monitoring the situation in Iran."

She said that Baqaie's threat to sever relations had not been made directly to the British Museum. "We have very strong relationships with colleagues in Iran and we hope that these will long continue."

Shapour Suren-Pahlav, programme director of the London-based Circle of Ancient Iranian Studies, applauded the museum's caution.

"The current regime in Iran is hostile to pre-Islamic Iran," he said. "The destruction of ancient sites has increased dramatically under Ahmadinejad, so I'm suspicious about why they want to borrow the cylinder. I suspect they might want to destroy it ‑ they don't like the current popularity of Cyrus. If the cylinder was lent to Iran, who could guarantee its safety?"