"Since it has become absolutely clear that the Italian prisoner is not involved in espionage for the infidels in Iraq, and in response to the call from the [Association of Muslim Scholars (AMS)], we in the Jihad Organisation will release the Italian prisoner in the coming days," the statement on Monday said.
It mentioned by name Giuliana Sgrena, a journalist with left-leaning Rome newspaper Il Manifesto, who was seized as she conducted interviews near Baghdad University on Friday.
The influential AMS had earlier called for her release.
It was not possible to verify the internet statement.
The claim was not accompanied by a picture or video of the captive or any identification papers.
The group, which also uses the name Islamic Jihad Organisation, on Friday set a 72-hour deadline for Italy to remove its troops to secure Sgrena's release.
On Sunday, it said it would kill her after 48 hours if its demands were not met.
Aljazeera urges release
From Qatar, Aljazeera issued a statement on Monday calling on armed groups in Iraq to free Italian and French journalists Giuliana Sgrena and Florence Aubenas.
The channel also expressed its support for the two reporters, saying that taking journalists hostage while they were performing their professional duties was a clear violation of human rights.
Italian Prime Minister Silvio Berlusconi's government has been an ally of the US in the Iraq war. But Il Manifesto was strongly opposed to the US-led invasion in 2003 and is an opponent of Berlusconi and US President George Bush.
The statement promising Sgrena's release repeated threats against Italy over its troop presence in Iraq.