The council organises cultural events for thousands of Iranians each year
The Iranian government says the British Council - which has suspended its activities in the country - was operating illegally there.
Iran said no contract had been signed with Britain allowing the cultural centre to operate in Tehran.
But the council says its work is fully compliant with international law.
The UK government expressed "great regret" over the closure and both governments say they are holding talks to try to resolve the situation.
The British Council announced on Wednesday that its Tehran centre had closed on 31 January.
Martin Davidson, the council's chief executive, told the BBC on Wednesday that most of its 16 local employees had been ordered to resign by the office of the Iranian president.
Mr Davidson said Iran has also denied visas for British staff for the past two years.
A statement from Iran's embassy in London says: "So far, no contract between the governments of the [Islamic Republic] of Iran and Britain has been signed on the British Council's activities in Tehran and any activities under this name are considered as illegal."
The two sides were discussing the issue, the statement added.
The council said in a statement: "The suggestion by the Iranian authorities that we are operating illegally is unfounded.
"The British Council has a legal basis to work in Iran and is compliant with international law."
"We would very much welcome discussions with the relevant authorities on resuming our work in Iran as soon as possible."
The British Council, while officially an independent non-profit charity, receives a large part of its funding from Britain's Foreign Office.
In a statement issued on Thursday, UK Foreign Secretary David Miliband said: "It is a matter of great regret that a country with Iran's culture should reject attempts to break down barriers and build cultural dialogue."
"The work of the British Council is completely non-political - it is focused on improving the relationship between our two countries by promoting mutual understanding and respect," he added.
Mr Miliband said the British government would continue to promote improved relations between the people of Iran and the UK.
The closure of the British Council in Tehran is the latest flare-up of tension between the two countries.
Last month, Iran warned the BBC's Tehran bureau against contributing to the network's newly launched Farsi language TV channel, which is banned from operating in Iran.
A major diplomatic row between the two countries erupted in March 2007 when Iran seized a group of 15 British sailors on a navy patrol near the waterway between Iraq and Iran.
The group was held for nearly two weeks before being released.
Iran has in the past accused Britain and the United States of plotting to overthrow the religious establishment, charges Washington and London deny.