"We believe strongly that there is no evidence to support any charge whatsoever," she said during a visit to Berlin.
"And we would renew our request on behalf of these three young people and their families that the Iranian government exercise compassion and release them so they can return home, and we will continue to make that case."
The families of the three Americans dismissed the charges.
"The allegation that our loved ones may have been engaged in espionage is untrue," they said in a joint statement.
"It is entirely at odds with the people Shane, Sarah and Josh are and with anything that Iran can have learned about them since they were detained on July 31.
"This has already gone on for too long."
The Iranian announcement came as Washington and its allies wait for Tehran's response to a deal over its nuclear programme under which it would send abroad low-enriched uranium.
Nazanine Moshiri, Al Jazeera's correspondent in Tehran, said: "They are talking directly, but only talking on the nuclear issue and only at a very low level.
"There are no diplomatic ties here and what the Americans have had to do to get to these three Americans is to go through the Swiss. The Swiss diplomats were able to visit them in Evin prison about a week ago."
Iran is also holding another American citizen, Kian Tajbakhsh, an academic who was arrested amid the mass protests over the re-election of Mahmoud Ahmadinejad, the president.
Last month he was sentenced to 12 years in prison for his alleged role in the violence that followed the polls.
In January, Roxana Saberi, an Iranian-American journalist, was arrested in Tehran, and convicted of espionage. She was later released on appeal.