It said in a statement that scientist Majid Taheri had been liberated after being detained in the US "for false reasons".

"Dr. Majid Taheri and Mr. White will soon be joining their families," Iran's top diplomat Mohammad Javad Zarif tweeted.

"This can happen for all prisoners," Zarif added. "Iranian hostages held in-and on behalf of-the US should come home."

White flew out of Iran on Thursday following US authorities' release of another Iranian scientist, Cyrus Asgari, who arrived home the day before, but both the arch-rival nations denied that was a swap.

Asgari, a scientist at Tehran's Sharif University of Technology, returned to Iran after spending nearly three years in detention due to espionage charges against him.

He was acquitted last year before being handed over to US Immigration and Customs Enforcement.

Asgari, 59, fell into the arms of his relatives on his arrival at Tehran's international airport, images broadcast by several Iranian media showed.

White's mother, Joanne White, announced the following day that her son "is safely on his way home".

White had tested positive for COVID-19 and received treatment in Iran, said Bill Richardson, a former US ambassador who said he met senior Iranian officials to win his release.

President Donald Trump hailed White's release and said he was returning home on an airplane sent by Switzerland, which represents US interests in Iran in the absence of diplomatic ties between the two countries.

White, who had served 13 years in the US Navy, was arrested in July 2018 in the northeastern city of Mashhad after visiting a woman whom he had reportedly met online.

He was sentenced the following year to at least 10 years in prison on charges that he insulted Iran's Supreme Leader Ayatollah Ali Khamenei and posted anti-regime remarks on social media under a pseudonym.

In March, as Iran was being hit hard by the coronavirus pandemic, White was handed over to Swiss custody and flown to Tehran but told not to leave the country.

Richardson said White, who is in his 40s and had pre-existing medical conditions, was admitted to a hospital for treatment but otherwise stayed at a hotel in Tehran.