The United States is unlikely to return to the Iran nuclear deal if four American citizens held by Tehran are not released, the lead U.S. nuclear negotiator said, after talks on reviving the 2015 pact appeared to have made some progress in recent days.

The U.S. has long insisted that the nuclear negotiations and the four Americans' custody are two separate issues, but in an interview with Reuters on Sunday, Special Envoy for Iran Robert Malley said a nuclear agreement with Iran could be contingent on their release.

"They're separate and we're pursuing both of them. But I will say it is very hard for us to imagine getting back into the nuclear deal while four innocent Americans are being held hostage by Iran," Malley said.

Washington accuses Iran of holding them hostage for diplomatic leverage, a charge Tehran has denied.

The two countries held negotiations on exchanging detainees last year but failed to strike a deal. Prisoner swaps between them are not uncommon, with one taking place on the first day of the nuclear deal, from which the U.S. withdrew in 2018.

"So even as we're conducting talks with Iran indirectly on the nuclear file we are conducting, again indirectly, discussions with them to ensure the release of our hostages," he said in Vienna, where talks on how to salvage the deal are ongoing.

Time seems to be of the essence if an agreement were to be reached between Iran and world powers. While U.S. and European officials said modest progress was made in the latest round of talks, they have repeatedly warned that time is running out.

Iran has said an agreement could be reached if there is guarantee that all sanctions imposed on the country will be lifted.