Ms Saberi has been in Iran for six years, working and doing research
A number of UK and US media outlets, including the BBC, have called on Iran to allow independent access to detained American journalist Roxana Saberi.
She has been in custody in Teheran since late January on unknown charges and allowed only one brief phone contact with her family.
Iranian officials have accused her of continuing to work in the country after her press credentials were revoked.
The authorities must specify how she broke the law, the media groups said.
A US-Iranian national, Ms Saberi has spent six years in Iran studying and writing a book.
She worked briefly for the BBC, and more recently filed reports for the US Fox News network and National Public Radio.
The open letter expresses deep concern about Ms Saberi's well-being and "the deprivation of her rights".
"We now ask that one or more international organizations that have responsibilities and rights under the Geneva Conventions be permitted access to Roxana immediately to ascertain her health and well-being and to determine the conditions under which she is held," it says.
It goes on to demand that any specific charges against her be made public.
"If no charges are filed, we now urge her immediate release and ask that she be given permission to return to her home country, the United States," it says.
Signatories include Vivian Schiller and David Westin, presidents of NPR and ABC News, Wall Street Journal editor-in-chief Robert Thomson, John Stack of FoxNews, and Jon Williams, who is World Editor at the BBC.