"The resistance refuses to be paid," the voice-over of the video shown by public RAI television and news channel Sky24 said on Tuesday.
The voice added, however, that a ransom had been proposed, but did not give details.
The suspected abductors also claimed that the United States had sought to kill Sgrena who was wounded when a US patrol opened fire on her vehicle on the road to Baghdad airport on Friday.
Italian intelligence officer Nicola Galipari, who had negotiated her release, was killed in the shooting incident.
"The insurgency learnt that the CIA wanted to kill Giuliana, the journalist", the voice said according to the Italian translation on Sky24.
"The insurgency's intelligence official warned the journalist," the voice said, adding: "Everything we're saying can be verified."
From her hospital bed, Sgrena (R)
said she may have been targeted
But the White House on Monday rejected as "absurd" suggestions that US soldiers in Iraq deliberately tried to Sgrena.
"It's absurd to make any such suggestion, that our men and women in uniform would deliberately target innocent civilians. That's just absurd," spokesman Scott McClellan told reporters in Washington.
Sgrena, the correspondent in Iraq of the Italian newspaper Il Manifesto, was kidnapped on 4 February and released last week.
Italy rejects US account
Italy's foreign minister rejected on Tuesday a US account of how its forces killed an Italian intelligence agent in Iraq and urged Washington to punish any soldiers found guilty of wrongdoing in the shooting.
"It is our duty to demand truth and justice," Foreign Minister Gianfranco Fini told parliament.
The US military appointed a general to head the investigation into the Sgrena shooting affair and opened a separate probe into a friendly fire incident that claimed the life of a Bulgarian soldier.
Brigadier General Peter Vangjel has been named to lead the probe into the incident on Friday, a military statement read.
The inquiry "is expected to take approximately three to four weeks to complete" over the incident, which happened less than an hour after Sgrena had been freed from a month-long hostage ordeal, the statement said.