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Iran's top diplomat on Sunday said "everything is ready" to implement a stalled prisoner exchange deal with the United States, which Washington promptly denied as a "cruel lie".

At least three US citizens are held in the country's prisons, according to Iran's judiciary and the US State Department.

"We have reached an agreement in recent days regarding the exchange of prisoners between Iran and the United States," Foreign Minister Hossein Amir-Abdollahian told state broadcaster IRINN.

The deal had been "signed and approved indirectly" last year, he added in a televised interview, saying the "American side is making its last technical arrangements" ahead of implementation.

"In our opinion, everything is ready," the minister said.

"If everything goes well on the American side, I think we will witness the exchange of prisoners in the short term."

State Department spokesman Ned Price called Amir-Abdollahian's claim that a deal had been reached "another especially cruel lie that only adds to the suffering of their (the prisoners') families".

"We are working relentlessly to secure the release of the three wrongfully detained Americans in Iran," Price added.

In October, Iranian media said a prisoner swap agreed by Tehran and Washington included the unfreezing of Iranian funds abroad, but Amir-Abdollahian on Sunday made no mention of that.

- Espionage charges -

The foreign minister's remarks came two days after a CNN interview with Siamak Namazi, an Iranian-American businessman held in Tehran's Evin prison since 2015.

Namazi, 51, was blocked from leaving the country during a visit and later sentenced to 10 years in jail on charges of collaborating with a foreign government.

He denies the accusations, which US officials have called groundless.

His father Mohammad Baquer Namazi, a former UNICEF official, was arrested in February 2016 when he went to Iran to try to free his son.

They were both sentenced to 10 years on spying charges in October 2016. Baquer, under house arrest since 2018, had his sentence commuted in 2020, and was finally granted permission to leave the country for medical treatment in October.

At least 16 Western passport holders, most of them dual nationals -- which Iran does not generally recognise -- are detained in the country.

Morad Tahbaz, an Iranian-American who also holds British nationality, was arrested alongside other environmentalists in January 2018 and sentenced to 10 years in jail for "conspiring with America".

Iranian-American venture capitalist Emad Sharqi was sentenced to 10 years in prison on spying charges, Iranian media reported in 2021, saying he was captured trying to flee the country.

Karan Vafadari, an Iranian-American member of the Zoroastrian minority faith, was arrested in June 2016 on allegations of spying and released on bail in July 2018. He is still unable to leave Iran.

Iran's judiciary reported in August "dozens" of Iranian nationals had been detained in the United States, including Reza Sarhangpour and Kambiz Attar Kashani who are accused of having violated US sanctions against Tehran.