Mr Talabani said the US had humiliated the Kurdish authorities by ignoring their laws and failing to consult them.
US officials said the man belonged to Iran’s Revolutionary Guards and that he was involved in smuggling explosives.
Both the Iraqi Kurds and Tehran insist the man was an Iranian trade official in Iraq on the invitation of the Kurds.
US-led forces seized the man in a hotel in the Kurdish city of Sulaimaniya on Thursday.
In a angry statement, Mr Talabani – who is himself a Kurd – said the arrest was made without the knowledge or co-operation of the Kurdish regional government.
“This amounts to an insult and a violation of its rights and authority,” said the statement, quoting from a letter Mr Talabani had sent the top US commander in Iraq Gen David Petraeus and US Ambassador Ryan Crocker on the day of the arrest.
The Iraqi president insisted that the man was part of a trade delegation – a guest of the Kurds – visiting to promote closer economic ties with Iran.
“I want to express to you our dismay over the arrest by American forces of this official civilian Iranian guest,” he said.
He said that Iran had threatened to close the border with the northern region if the Iranian official was not freed.
‘Regrettable incident’
On Friday, the president of the Kurdish regional government, Massoud Barzani, said the arrest was illegal.
The Americans “must release this individual as quickly as possible because this kind of attitude does not serve the common interest”, he said in a statement.
The US has accused the elite Quds Force of Iran’s Revolutionary Guards of helping arm Shia militias in Iraq. Iran denies any involvement with militants.
It is the second such incident in Iraqi Kurdistan this year.
Tehran is still demanding the release of five Iranians seized in the city of Irbil in January who the US says have links to the Revolutionary Guard and were training militants in Iraq.
In August, the US military admitted to what it called a “regrettable incident” after it arrested a group of eight Iranians in Baghdad.
They were freed after the Iraqi government intervened.
