Namazi, a former UNICEF official, was detained in February 2016 when the 85-year-old travelled to Iran to press for the release of his son Siamak, who had been arrested in October of the previous year.

"Mohammad Baquer Namazi, who had been released from prison a few days ago, left Iran today (Wednesday)," the state broadcaster said, posting footage of Namazi boarding a plane in Iran.

The United States has been pressing for the release of the Namazis and two other Americans amid efforts to revive the 2015 nuclear deal between Iran and major powers.

"Wrongfully detained US citizen Baquer Namazi has been permitted to depart Iran, and his son Siamak, also wrongfully detained, has been granted furlough from prison," a State Department spokesperson told AFP.

The spokesperson said that previously the older Namazi was "not permitted to leave the county after serving his sentence, despite his repeated requirement for urgent medical attention."

The United Nations said last week that the pair had been allowed to leave Iran, after an appeal from Secretary General Antonio Guterres.

Both were convicted of espionage in October 2016 and sentenced to 10 years in prison.

Baquer Namazi was released on medical leave in 2018 and had been serving his sentence under house arrest.

At least two other American citizens are currently held in Iran.

Businessman Emad Sharqi was sentenced last year to 10 years in prison for espionage, and environmentalist Morad Tahbaz, who is also a British national, was arrested in 2018 and released on bail in July.

- Iran eyes frozen assets -

A drive to salvage the 2015 nuclear deal began in April last year, with the aim of returning the United States to the accord through the lifting of sanctions reimposed by president Donald Trump in 2018 and Iran's return to full compliance.

The signing of the original deal was accompanied by the release of detained Americans and Namazi's departure has been seen in Iran as a move that should be mirrored by the other side.

"With the finalisation of negotiations between Iran and the United States to release the prisoners of both countries, $7 billion of Iran's blocked resources will be released," state news agency IRNA reported.

But the US State Department on Sunday dismissed the reported link as "categorically false".

Billions of dollars in Iranian funds have been frozen in a number of countries -- notably China, South Korea and Japan -- since the US reimposed sanctions.