The United States on Sunday rejected Iranian reports that Tehran's release of two detained Americans will lead to the unfreezing of Iranian funds abroad.

Baquer Namazi, 85, was permitted to leave Iran for medical treatment abroad, and his son Siamak, 50, was released from detention in Tehran, the United Nations said on Saturday.

Now Iran is awaiting the release of about $7 billion in funds frozen abroad, Iranian state media said Sunday.

"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," the state news agency IRNA said.

But the US State Department dismissed any such link as "categorically false."

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

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

Billions of dollars in Iranian funds have been frozen in a number of countries -- notably China, South Korea and Japan -- since the United States reimposed biting sanctions on the Islamic republic in 2018 after unilaterally withdrawing from Tehran's nuclear deal with world powers.

Tehran has accused Seoul of holding $7 billion of its funds "hostage", repeatedly calling on South Korean authorities to release it.

IRNA on Sunday said that "Washington is pursuing at the same time the release of its citizens detained in Tehran and the release of Iranian funds in South Korea".

The development comes as on-off talks have been underway since April 2021 to revive the 2015 deal that gave Iran much-needed sanctions relief in return for curbs on its nuclear programme.

Iran has repeatedly called for the lifting of sanctions, as well as guarantees that the United States will not again pull out of a revived deal.

Baquer Namazi is a former UNICEF official who was detained in February 2016 when he went to Iran to press for the release of his son Siamak, who had been arrested in October of the previous year.

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

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