The US and Iran have freed five detainees each in a controversial prisoner swap involving the unfreezing by the Biden administration of $6bn (£4.8bn) of Iranian oil money.

In an elaborate and delicate diplomatic deal, months in the making, the five Americans – some held for nearly a decade – were taken from hotels in Tehran to a plane that flew to Qatar, before heading back to Washington.

“Today, five innocent Americans who were imprisoned in Iran are finally coming home,” Joe Biden said in a statement. The US president added that they “will soon be reunited with their loved ones – after enduring years of agony, uncertainty and suffering”.

The US secretary of state, Antony Blinken, said he had spoken to the freed US citizens by telephone in what he said was “an emotional conversation”.

Among the prisoners is the conservationist Morad Tahbaz, a British-American citizen. Iranian state media confirmed on Monday afternoon that five Iranian citizens imprisoned in the US – mostly for sanctions-busting offences – were also released. Only two of the five released Iranians have chosen to return to Iran.

Qatar has been acting as the mediator for the deal, commencing with the electronic transfer of the Iranian cash to bank accounts in Qatar and Switzerland. The prisoners were allowed to board the plane only after the cash transfer was completed. Apart from Tahbaz, the identities of only two other Americans have been made public.

It is not clear if the deal will lead to a wider diplomatic breakthrough, or a new, less ambitious route to constrain Iran’s civil nuclear programme, in which Tehran agrees to lower its stocks of highly enriched uranium.

Fatemeh Aman, a senior fellow at the Washington-based Middle East Institute, said: “It’s a positive act and many countries at odds with one another have had this kind of deal. However, this does not mean the end of Iran-US animosity. The hardline government of Iran may declare it a victory, but other major issues, such as the Iran nuclear dilemma, will not go away so easily. I believe some hardline factions need ‘death to America’ for their existence.”

Iran’s president, Ebrahim Raisi, said on Monday that the release of the detainees by Tehran was “purely a humanitarian action … in the future other humanitarian actions can be taken”.

He added: “Unfortunately history has shown the lack of trust towards the United States because it has trampled upon commitments and broken promises repeatedly.”

Republican senators in the US and some former Iranian political detainees have accused Biden of striking a deal that will only encourage Iran to keep hostage-taking as a central part of its diplomatic arsenal. The US state department says the money that is being released is oil money owed to Iran and frozen by the Trump administration in 2018 when the US left the Iran nuclear deal.

Last week, three European countries, including the UK, accused Iran of building stocks of highly enriched uranium that could have no possible civilian purpose.

The US says Qatar will ensure that the unfrozen money is only spent on goods – primarily food, agricultural goods and medicine – that are not subject to sanctions. However, critics say it will be impossible to police.

Brett McGurk, the national security coordinator for the Middle East, defended the deal to the Washington Post newspaper, saying: “The president ultimately needs to weigh the terms available through diplomacy against leaving American citizens for years or even decades in Evin prison. In this case, the president made the hard decision to move ahead.”

The path to the swap reached a turning point recently when the state department agreed a waiver facilitating the release of the cash from South Korean banks to accounts in Switzerland and Doha.

The five Americans were previously transferred out of Evin jail in Tehran to various hotels in the capital.

Tahbaz was left in Iran when the British-Iranian dual nationals Nazanin Zaghari-Ratcliffe and Anoosheh Ashoori were released as part of a deal negotiated by the then UK foreign secretary, Liz Truss.

The rights group Amnesty International said it was delighted for Tahbaz and his family “who’ve campaigned tirelessly for his release, often battling with UK officials who’ve never treated Morad’s plight with anywhere near the urgency and seriousness it merited”.

The deal is a diplomatic win for Qatar as a mediator between two countries that deeply distrust one another. The Iranian president, due to speak to the UN general assembly on Tuesday in New York, is likely to laud the deal as another sign of US weakness.

Michael McCaul, the Republican chair of the US House foreign affairs committee, has accused Biden of being naive and returning to the mistakes of the past.

The Republican presidential contender Ron DeSantis described Biden’s decision as outrageous, adding that it “has sent a signal to hostile regimes that if you take Americans, you could potentially profit … A rogue regime should know that if you touch the hair on the head of any American, you will have hell to pay.”

Richard Ratcliffe, the husband of Nazanin Zaghari-Ratcliffe, has criticised the timing of the release, so close to the anniversary of Mahsa Amini’s death in Iranian police custody.

Iranian-Americans, whose US citizenship is not recognised by Tehran, are often pawns between the two nations. In the last week, there have been reports that three dual nationals were arrested in Iran. It was confirmed two weeks ago for the first time that Johan Floderus, an EU diplomat who travelled to Iran, has been jailed since April 2022.