The group said in a statement sent to Aljazeera along with a videotape on Wednesday that it had killed the hostage because the Italian president Silvio Berlusconi said pulling his troops out of Iraq was "not in question."
Responding to the news of the killing, the Italian president, however, insisted his resolve was firm and unchanged.
"They have destroyed a life, they have not cracked our values and our efforts for peace," the Italian president said.
Aljazeera earlier described the tape as "too bloody" and said it will not air it "in order not to upset viewers sensitivities".
In a statement accompanying the tape, the abductors of the four Italians justified the killing.
"When your president says pulling the troops out of Iraq is non-negotiable then this means he does not care for the safety of his citizens as much as he is concerned with satisfying his masters in the White House," the statement said.
"They have destroyed a life, they have not cracked our values and our efforts for peace"
"We have killed one of the four hostages we have in order to teach a lesson for those who are involved. We know they are guards working for the American occupation in our country.
"We ask you one more time to revolt once again in the face of your leaders and reject this unjust war on us so that we can protect your citizens. We are waiting for that from you or else we will kill them one by one," added the Green Brigade.
While confirming the death of one of the four hostages, Italian Foreign Minister Franco Frattini identified the killed hostage as Fabrizio Quattrocchi.
A former baker, Quattocchi,35, was shot in the back of the neck with a pistol.
Asked about the possible fate of the other hostages, the minister said "he did not know."
"Our duty is to do everything we can to get them out of there," he added.
Aljazeera aired a videotape on Tuesday showing the four Italians, with their passports, surrounded by armed men.
The group member said on videotape that they would hold the Italians until their demands are met, including withdrawal of Italian troops from Iraq, the release of Imams and an apology from Rome.
Silvio Berlusconi said on Tuesday the withdrawal of his country's 3000 strong military force in Iraq was "absolutely not in question".