Namazi, a former UNICEF official, was detained in February 2016 when he 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 Iranian state broadcaster said, posting footage of Namazi boarding a plane.

Human rights lawyer Jared Genser later confirmed via Namazi's cousin who travelled with the 85-year-old on the plane that he had arrived in Muscat, Oman's capital.

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.

His son Siamak, "also wrongfully detained", has been given furlough from prison but remains in Iran, a State Department spokesperson told AFP.

"Baquer Namazi was unjustly detained in Iran and then not permitted to leave the county after serving his sentence, despite his repeated requirement for urgent medical attention," the spokesperson said.

"We understand that the lifting of the travel ban and his son's furlough were related to his medical requirement."

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

- Iran eyes frozen assets -

The Namazis were 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.

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.