Saberi, 31, holds dual citizenship and was working as a freelance journalist in Iran.
She was arrested in late January, initially accused of working without press credentials. She told her father in a phone conversation that she was arrested after buying a bottle of wine, which is illegal in the country.
Robert Wood, the US state department spokesman, on Tuesday called the charges against Saberi "baseless and without foundation" and demanded her immediate release.
"We continue to work for her release," he said.
Wood said that Hillary Clinton, the US secretary of state, checked every day on Saberi's status.
Few details have been released about the charges against Saberi and Jamshidi criticised the US for commenting on the case.
"Giving an opinion on a case, by an individual or a government, without being informed about the facts in it, is utterly ridiculous," he said.
Espionage can carry the death penalty under Iran's penal code, but those convicted of spying normally face up to 10 years in prison.
Reza and Akiko Saberi, Saberi's parents, met her in the Evin prison on Tuesday.
"We are waiting for the judge to make a decision ... There is always hope. But we don't know what will happen"
"We met Roxana today for a few minutes and she is doing well," her father told the AFP news agency.
"We are waiting for the judge to make a decision ... There is always hope. But we
don't know what will happen."
Last week, Hassan Haddad, Tehran's deputy prosecutor, said Saberi was carrying out "spying activities under the guise of being a reporter".
"The evidence is mentioned in her case papers and she has accepted all the charges."
After meeting her earlier this month, Saberi's father told National Public Radio she wanted to see her lawyer to point out that some of the statements she made were "under pressure, under threat."
The US-born journalist has been working in Iran for six years, reporting for the BBC, Fox News and other media. Her father said she was working on a book when she was arrested.
Karim Sadjadpour, an Iran expert at the Washington-based Carnegie Endowment for International Peace, said it was not a coincidence that the charges against Saberi come as Obama is trying to establish better relations with Iran.
"There are powerful hard-line factions in Tehran who do their best to torpedo or sabotage efforts to improve [US-Iran] relations because they stand to lose both politically and financially, and I think I would put Roxana's case in that context.''
Since taking office earlier this year, Obama has pledged to change Washington's Iran policy. The US broke off diplomatic relations with Iran after the 1979 Islamic Revolution.
Sadjadpour said Washington needs to handle the Saberi case delicately.
"The [US] government clearly wants to express its concern. But on the other hand, too much emphasis on her case might not be in the interest of Roxana's expeditious release because Iran may feel like they do not want to appear to be giving in to US pressure,'' he said.
Human rights groups have repeatedly criticised Iran for arresting journalists and suppressing freedom of speech.
The government has arrested several Iranian-Americans in the past few years, citing alleged attempts to overthrow its Islamic government. They were never put on trial and were eventually released from prison.