Al-Arabiya TV has broadcast a new tape, purportedly from militants threatening to kill three Italians held in Iraq.
Footage of the men has been shown on Italian state TV
The Arabic channel reported that the captors said they would release the hostages if protests were held in Italy against the country's presence in Iraq.
The group, calling itself the Green Battalion, reportedly set a five-day ultimatum for the rallies to be held or the men would be killed.
The Italian prime minister has not commented on the broadcast.
But spokesman Paolo Bonaiuti said Silvio Berlusconi was "following developments minute by minute".
One of the hostages' colleagues, abducted with them, was killed two weeks ago.
Fabrizio Quattrocchi became the first foreign captive known to have been executed in the recent spate of hostage-taking across Iraq.
A number of civilians have been released but hostages of various nationalities, including a US soldier, are still being held.
The videotape, broadcast by the Dubai-based al-Arabiya channel, showed three bearded men, sitting behind a small table, eating from a large pot with their fingers.
The BBC's Frances Harrison, in Rome, says the showing of the video on Italian state television was an emotional moment for the hostages' families - joy that they were still alive mixed with the realisation of the seriousness of the captors' threats.
"Now we have one certainty, that they're alive," Christian Stefio, the brother of hostage Salvatore, told Reuters news agency.
"We have seen that they're well and that has encouraged us," said Umberto Cupertino's cousin Laura Albanese.
The leaders of all Italy's main political parties rejected the kidnappers' demands.
"We who are opposed to the war are totally against any negotiations with the kidnappers and terrorists," centre-left opposition leader Francesco Rutelli told AFP news agency.
Marco Follini of Mr Berlusconi's coalition partner the UDC described the broadcast as a "message from another planet".
"A serious country cannot accept blackmail," he said.
The militants who executed Mr Quattrocchi had earlier threatened to kill the three other Italians "one by one" but last week there were optimistic declarations from officials in Rome that negotiations could bring about a release.
The Italians, abducted on 12 April as they left Baghdad in a taxi, had been working as security guards for a US-based company.
Rome, which has been a strong ally of the US under Prime Minister Silvio Berlusconi, sent about 3,000 troops to Iraq for reconstruction and humanitarian missions after the end of the war.
Huge public demonstrations against an invasion of Iraq were held in Italy before the war and opinion polls indicate declining support for the deployment of Italian forces there now.
But Mr Berlusconi has said Italian forces will remain in Iraq beyond the planned transfer of power on 30 June.