DUBAI, United Arab Emirates — Iran’s top diplomat claimed Sunday that a prisoner swap was near with the America, though he offered no evidence to support his assertion. American government officials immediately dismissed his comments as a “cruel lie.”

The Iranian Foreign Minister, Hossein Amirabdollahian, has made similar comments in the past about possible deals with America on frozen assets abroad and other issues that never came to fruition. Some of those remarks have appeared aimed at shoring up domestic support amid the mass protests challenging Iran’s theocracy and supporting the country’s troubled rial currency.

However, in an interview Sunday with Iranian state television, Mr. Amirabdollahian claimed that Iran had “reached an agreement in recent days regarding the exchange of prisoners between Iran and the United States.”

“If everything goes well on the American’s side, I think we will see the exchange of prisoners in the short term,” he added. He alleged a document between Iran and America laying out the exchange had been “indirectly signed and approved” since March 2022.

Reached by the Associated Press, the U.S. State Department spokesperson, Ned Price, called the comments “another especially cruel lie that only adds to the suffering of their families.”

“We are working relentlessly to secure the release of the three wrongfully detained Americans in Iran,” Mr. Price said. “We will not stop until they are reunited with their loved ones.”

A separate statement from the White House’s National Security Council also called the remarks “false.”

“Unfortunately, Iranian officials will not hesitate to make things up, and the latest cruel claim will cause more heartache for the families of Siamak Namazi, Emad Shargi and Morad Tahbaz,” the council said, naming the three Americans known to be held by Tehran on widely disputed espionage charges.

Iran long has taken prisoners with Western passports or ties to use in negotiations with foreign nations.

The evidence against them has never been made public. The detainees all have dual American-Iranian citizenship, something Tehran does not recognize.

In recent days, however, Mr. Namazi was allowed to conduct an interview with CNN from Tehran’s notorious Evin prison — something that would not have happened without the acquiescence of security forces.

Meanwhile, a deputy Iranian foreign minister who has handled nuclear talks with world powers, Ali Bagheri Kani, made a trip Sunday to Oman, a longtime interlocutor between Tehran and Washington.

Mr. Amirabdollahian’s comments also come after Iran and Saudi Arabia, with Chinese mediation, announced Friday they would reestablish diplomatic ties and reopen embassies after a seven-year freeze in relations.

Associated Press. Matthew Lee in Washington contributed to this report.