TEHRAN, IRAN -- Iran said on Tuesday that American authorities are holding about 20 Iranian nationals in jail, its official news agency reported, a day after Tehran said it was ready for more prisoner swaps with the U.S.

A prisoner exchange over the weekend saw Iran free a Chinese-American scholar from Princeton who had been held for three years on widely criticized espionage charges. It was seen as a rare diplomatic breakthrough between Tehran and Washington after months of tensions.

"We told the American side that our figure is more or less 20 but this is not final," IRNA quoted as saying Mohsen Baharvand, an aid to Iran's foreign minister. The report didn't provide further details on the claim.

According to Baharvand, U.S. authorities say that Iran is holding one American national and five dual U.S.-Iranian nationals. He said Iranian officials didn't have "any orders" so far to begin talks on their release, though he suggested this could be the next "phase" in indirect negotiations between Tehran and Washington.

U.S. citizens held in Iran include U.S. Navy veteran Michael White, who is serving a 10-year espionage sentence, as well as environmentalist Morad Tahbaz, an Iranian with U.S. and British citizenship also initially sentenced to 10 years in prison.

Baharvand said Iran didn't undertake direct talks with the U.S. for the weekend's prisoner swap in Switzerland. The two sides only communicated through Swiss officials, who represent U.S. interests in Iran. Washington and Tehran have had no diplomatic ties since the 1979 Islamic revolution.

Others with Western ties held in Iran include two French researchers, Roland Marchal and dual Iranian national Fariba Adelkhah. Their lawyer, Saeed Dehgan, told The Associated Press on Tuesday that Iranian prosecutors have defied a judge's ruling that the two academics could be released on bail.

Iranian officials disclosed in July the arrest of Adelkhah, a prominent anthropologist who often travelled to Iran for her research on post-revolutionary Iranian society. They said she was arrested on espionage charges.

Iran does not recognize dual citizenship for its nationals.

In October, France revealed that Marchal had also been arrested.

Tensions have risen sharply over Iran's unraveling nuclear deal with world powers, which France still supports. U.S. President Donald Trump unilaterally withdrew from the accord over a year ago, before re-imposing crippling sanctions on Iran's economy.