But his government has insisted it will not bow to pressure from the captors of an Italian journalist who have demanded a troop withdrawal from Iraq.
Frattini's message was delivered on Thursday, one day after the family of Italian journalist Enzo Baldoni appealed to his Iraqi captors, via Aljazeera, to release him.
"We are ready to pull out of Iraq, even tomorrow, if the government of Mr Allawi asks us," said Frattini, speaking just hours ahead of the expiry of a deadline set by Baldoni's captors for Italy to withdraw its 3000 troops from Iraq.
The Italian government had earlier rejected the captors' ultimatum, affirming that it would maintain its "civil and military" presence in Iraq and stressing that it was doing everything possible to secure the hostage's release.
But Frattini said that Rome "respects the Allawi government, which has credibility".
Italy "respects what it decides in all freedom. If the Allawi government asks us to take Iraqis into our hospitals or to build schools, as we have already done, we will continue to do it," he said.
Baldoni disappeared last week on the road to the troubled central city of Najaf. A group calling itself the Islamic Army in Iraq on Tuesday released video footage of the journalist and gave Rome 48 hours to announce it was pulling its troops out.
In the video which was aired by Aljazeera, the captors said they "cannot guarantee the Italian's safety ... if Italy does not respond within 48 hours with a decision to withdraw its troops from Iraqi territories".
The captors gave Rome 48 hours
to announce its Iraq withdrawal
The group lashed out at Italian Prime Minister Silvio Berlusconi over what it called "his positions hostile to Islam and his insistence on continuing to participate in the war on Iraq".
In their televised appeal, Baldoni's children - Gabriella, 24, and Guido, 21 - said he was a man of peace who had done no harm to anyone.
Addressing the Iraqi people and his captors, Gabriella said: "We simply want to say that Enzo Baldoni is in Iraq as a man of peace as well as a journalist.
"He tried to save lives at Najaf, offering his help to a convoy of the Italian Red Cross, in the spirit of solidarity that has always inspired his thoughts and his spirit."
The journalist was on assignment in Iraq for Italian weekly Diario.
The Islamic Army in Iraq has claimed responsibility for the capturing of an Iranian diplomat who went missing in Iraq earlier this month. It was also blamed for the execution last month of two Pakistani workers taken captive.
Dozens of foreigners have been taken captive in Iraq by armed fighters resisting the US-led multinational occupation with the aim of putting pressure on their governments or employers to leave the war-torn country.