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Tehran has detained a number of US-Iranian dual citizens and Iranians with US permanent residency in recent years, most of them on "trumped-up" spying charges.

During an interview with CBS News' "Face the Nation" programme, Sullivan was asked about the Americans being held in Iran.

"We intend to very directly communicate with the Iranians about the... unjust, unlawful detention of American citizens in Iran," he responded.

He explained that the US was already communicating with the Iranians on the matter and will continue to do so.

"And our strong message to the Iranians will be that... we will not accept a long-term proposition where they continue to hold Americans in an unjust and unlawful manner. It will be a significant priority of this administration to get those Americans safely back home," he told the broadcaster.

The interview then moved on to talking about the reviving of nuclear .

Sullivan pointed out that "diplomacy is the best way to do it... but what's happened as a result is that the script has been flipped.

"It is Iran that is isolated now diplomatically, not the United States. And the ball is in their court."

The US said last week that it was open to talks with Iran about a return to the 2015 nuclear agreement, which was abandoned by the Trump administration.

The deal aimed at keeping checks and balances on Iran's nuclear programme in exchange for the  of most international sanctions on Tehran.

Tehran has repeatedly said it's ready to return to its nuclear commitments on the condition that Washington makes the first move by lifting sanctions on Iran.

UN nuclear watchdog chief was in Tehran on Sunday, ahead of a deadline set by Tehran to restrict the agency's inspections of nuclear sites unless the  lifts sanctions.

Iran said that there had been "fruitful discussions" on the issue.

After Sullivan remarks on CBS News, Iran's foreign ministry spokesman Saeed Khatibzadeh said that "this news is not true as stated and there is no direct dialogue between Iran and the United States in any field".

"Our priority is the release of Iranian prisoners in the United States," she added, according to the Iranian Students News Agency.

Iranian-American businessman Emad Shargi is the latest dual citizen to be detained in Iran and was given a 10 years jail sentence over alleged spying charges.

As of April 2020, at least 12 dual and foreign nationals or Iranian citizens who've lived and worked overseas were known to be imprisoned in Iran according to research by the Center for Human Rights in Iran (CHRI).

"Iran has used imprisoned dual nationals as bargaining chips in its dealings with other nations. The Iranian judiciary"s ongoing imprisonment of these women and men [...] also reflects Iranian hard-liners' efforts to prevent Iran's engagement with the West," the CHRI said.