Deputy Foreign Minister Hassan Ghashghavi's comments concerned reporter Jason Rezaian and a photographer, both of whom are dual US-Iranian citizens and were arrested on July 22.
"We do not accept dual nationalities. If a person enters Iran with an Iranian passport, that person is considered an Iranian citizen," Ghashghavi told Vatan-e-Emrooz, a prominent conservative daily.
"And we do not allow other countries to demand consular rights on behalf of Iranians," he was quoted as saying Wednesday.
Rezaian's wife Yeganeh Salehi, who is also a journalist, was arrested in the same incident. She is Iranian but is reported to have recently applied for permanent US residency.
The United States, which has no diplomatic ties to Iran, has called for the journalists to be freed.
A State Department spokeswoman said America had reached out to the Swiss embassy in Tehran, which acts as a go-between, to try to ensure consular officials can visit Rezaian.
It is still not known where the journalists are being held.
But Ghashghavi said: "So far, we have not received a letter requesting freedom for these journalists, but as it is about journalists, the matter could be followed up through foreign diplomatic channels."
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Iranian authorities have not said why Rezaian and his colleagues were arrested, but confirmed that the case is under investigation.
Ghashghavi's comments broke a near news blackout.
The only previous official statement about Rezaian, Salehi and the photographer, whose family have asked that her identity not be disclosed, hinted at espionage, but made no specific allegations.
"The security forces have the whole country under surveillance and control the activities of enemies," said Tehran chief justice Gholamhossein Esmaili, three days after the arrests.
"They will not permit our country to become a land where our enemies and their agents carry out their activities," he added.
A columnist for Vatan-e-Emrooz has alleged that Rezaian is being held for being the director of a video of US singer Pharrell Williams' hit song "Happy" that went viral in May, sparking a political row and eventually leading to the clip's participants being arrested.
Recorded on a smartphone and uploaded on YouTube, it showed three Iranian girls not wearing the mandatory veil, dancing and singing along to the song on rooftops and in secluded alleys with three young men.
The same columnist accused Rezaian of acting as a liaison for the National Iranian American Council (NIAC), a Washington-based lobby group. None of the allegations was substantiated.
The Washington Post has appealed to Iran for the journalists to be released, noting that Rezaian's reporting from the Islamic republic has conveyed events in a responsible manner.