TEHRAN (Reuters) - Iran's investigation of Iranian-American freelance journalist Roxana Saberi has been completed and she will be freed soon, a official from the prosecutor's office said on Friday.

Saberi, a 31-year-old who was born in the United States and who has reported for the BBC, National Public Radio and other media, was detained in the Islamic state more than a month ago.

U.S. Secretary of State Hillary Clinton demanded that Tehran immediately release the journalist during a news conference on Thursday at NATO's headquarters in Brussels.

She earlier said the United States planned to invite Tehran to a conference on Afghanistan, in a first overture to Iran.

The United States is reviewing its isolation policy on the Islamic Republic, including whether to open up a low-level diplomatic office there.

Iran's judiciary said this week that Saberi was being held in Tehran's Evin prison on the orders of a revolutionary court, which under Iran's legal system deals with state security as well as other issues.

Investigations with her have taken place and she will be released in the next few days, an official from Tehran's public prosecutor's office was quoted as telling ISNA news agency.

Judicial officials were not immediately available to comment.

A Foreign Ministry spokesman had said Saberi was working illegally after her press card was withdrawn two years ago.

Saberi's father Reza said from Fargo, North Dakota, on Sunday that she had been held in Iran since January 31, ostensibly for buying a bottle of wine. Buying alcohol is banned under Iran's Islamic law.

He confirmed her credentials as a correspondent had been revoked but said she had stayed in Tehran to pursue a master's degree and was doing research for a book about Iranian society.

(Writing by Zahra Hosseinian, Editing by Alison Williams)

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