The Babylonian clay cylinder dates from the sixth century BC
Iran has said it will cease cultural co-operation with the British Museum if a treasure is not lent to the nation.
The Cyrus Cylinder is being held by the museum because of Iran's "post-election situation", an Iranian official told the country's Fars news agency.
Hamid Baqaie said the museum's pledge to send the Babylonian artefact at another date was "just an excuse".
The British Museum said its trustees "reaffirmed their intention to lend the Cylinder to Iran".
Their statement added: "There are a number of issues and practicalities to be resolved, but the intention is to send it as agreed."
Speaking to the Guardian newspaper recently, the British Museum's head of press Hannah Boulton said: "When lending any material you have to check that it is an appropriate moment.
"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 added.
Mr Baqaie said Iran's Cultural Heritage Organisation would consider severing ties with the British Museum if the piece was not loaned to them within two months.
He added that it was due to have been lent last month.
The object, which is around 2,500 years old, was ordered to be made by Persian king Cyrus following the conquest of Babylon.
It is said to represent the first bill of rights and encapsulate religious toleration.