President Donald Trump voiced hope for progress with arch-rival Iran on Thursday after the clerical regime released a US Navy veteran and the United States freed two Iranians.

Michael White, who had contracted the coronavirus while in Iran, flew out on a Swiss military jet to Zurich where he was welcomed by a senior US official.

"I am blessed to announce that the nightmare is over, and my son is safely on his way home," his mother, Joanne White, said in a statement.

Trump said he spoke to White by telephone and voiced rare appreciation to Iran, with which the United States was close to all-out war several months ago.

"Thank you to Iran, it shows a deal is possible!" Trump wrote on Twitter.

As White was flying home, a federal judge issued an order to free an Iranian-American doctor, Majid Taheri, allowing him to go see family in Iran.

A day earlier, a more prominent Iranian — Cyrus Asgari, a scientist arrested in 2016 while on an academic visit — returned to Iran.

"This can happen for all prisoners. No need for cherry picking," Iranian Foreign Minister Mohammad Javad Zarif wrote on Twitter.

"Iranian hostages held in — and on behalf of — the US should come home," he said.

US Secretary of State Mike Pompeo, who has championed a hawkish line against the clerical regime, said Iranian authorities had been "constructive" on freeing White but urged the release of three other US citizens, all of Iranian descent, who remain detained.

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 the custody of Switzerland, which handles US interests in the country in the absence of diplomatic relations.

Iranians allowed to leave

Asgari, a scientist at Tehran's Sharif University of Technology, had been detained four years ago on an academic visit to Ohio and accused of stealing trade secrets.

He was acquitted last year but handed over to US Immigration and Customs Enforcement, which Asgari said refused to let him leave and held him in a lockup in Louisiana without basic sanitation.

Denying a connection with White, senior US immigration official Ken Cuccinelli alleged that the Iranians had held up his release, tweeting: "A swap can't exactly work when we want Asgari less than the Iranians do."

But the timing was even more clearly linked with Taheri, a doctor in Tampa, Florida, with a judge releasing him Thursday on time served.

Asgari, a scientist at Tehran's Sharif University of Technology, had been detained four years ago on an academic visit to Ohio and accused of stealing trade secrets.

He was acquitted last year but handed over to US Immigration and Customs Enforcement, which Asgari said refused to let him leave and held him in a lockup in Louisiana without basic sanitation.

Denying a connection with White, senior US immigration official Ken Cuccinelli alleged that the Iranians had held up his release, tweeting: "A swap can't exactly work when we want Asgari less than the Iranians do."

But the timing was even more clearly linked with Taheri, a doctor in Tampa, Florida, with a judge releasing him Thursday on time served.

He was accused of violating US sanctions by sending a technical item to Iran and in December pleaded guilty to charges he violated financial reporting requirements by deposing $277,344 at a bank, repeatedly showing up with loose cash, according to court documents.

Taheri was working for a Tampa clinic, since shut down, whose owner was earlier indicted on charges of prescribing painkillers without medical purposes.

Soaring tensions

Tensions have soared in recent months as Trump pursued a "maximum pressure" campaign against Iran, imposing sweeping sanctions and in January ordering a drone strike that killed a top Iranian general.

Observers have seen prisoner releases as a rare way of starting dialogue between the two countries, although few expect any serious headway before the US election in November.

White's mother thanked both the US and Swiss governments for the release as well as Bill Richardson, a former US ambassador and governor from the Democratic Party.

Richardson, whose efforts have been resented by the Trump administration, said he met senior Iranian officials including Zarif to arrange White's release.

Richardson in a statement said that his approach relies on "personal relations and respect."

"The negotiations were complicated, especially given the high tensions and exchange of violence between the US and Iran in recent months," said Richardson, who added that Qatar — a US ally that maintains stable relations with Iran — also provided assistance.

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