The official also confirmed "there are active discussions, indirect discussions," underway with Tehran to secure the "immediate" release of US citizens being held in Iran, but did not say if that was a condition for a US return to the accord.

Indirect negotiations began in early April in Vienna between Washington and Tehran, with the other signatories to the 2015 deal -- Britain, China, France, Germany, Russia and the European Union -- acting as intermediaries.

The goal is to find a way back to the accord known by its acronym JCPOA, which former US president Donald Trump walked away from and which his successor Joe Biden wants to revive.

For that to happen, the United States and Iran must agree on the lifting of the sanctions reinstated by Trump and on Tehran's commitment to follow the terms of the deal.

Once Trump walked away from the 2015 agreement, the Islamic republic started to abandon the constraints on its production of nuclear material.

- 'Productive' talks -

The three initial rounds of talks were described as "serious" and "productive" by the US official, who asked not to be named.

Russia has said it wants an agreement concluded in a fortnight, before the campaign for Iran's June 18 presidential election overshadows the talks. Washington has not ruled out this possibility.

"Is it possible to get a deal before the Iranian elections? Absolutely," said the State Department official.

"It's doable because this is not rocket science -- it's not inventing a new deal, it's reviving one that has been undermined," the official said.

The official admitted the main variable in the equation was how much Iran's leadership really wants to achieve an agreement.

"If Iran makes a political decision that it genuinely wants to return to the JCPOA as the JCPOA was negotiated, then it could be done relatively quickly and implementation could be relatively swift," he said.

"We don't know if Iran has made that decision," the official said.

That question may be answered in Friday's talks, the official said, noting: "We'll just have to see whether the next round actually moves things forward or whether we still are faced with unrealistic demands by Iran."

- Prisoner release deal? -

In parallel with the nuclear talks, Iranian media reported last weekend that there was an agreement between Tehran and Washington for the release of prisoners held by each side.

Despite the detailed reports, both sides now deny such an accord.

"There's no deal," an US official said, accusing Iran of "unspeakable cruelty" for putting out stories that raised the hopes of families of those held.

Nevertheless, the official said, "we want it to be resolved sooner rather than later. . . We want to deal with the detainees immediately."