Iraq's ambassador to the Holy See, Habeeb Al Sadr, said the pontiff would be under threat in the Muslim country from militant group Islamic State (IS).
IS has been advancing over parts of Iraq and Syria and has already killed thousands of Christians, with many more forced from their homes.
Pope Francis will spend Sunday in Albania and Al Sadr said there was a real risk to the Holy Father's life.
He told Italian newspaper La Nazione: "What has been declared by the self-declared Islamic State is clear - they want to kill the Pope. The threats against the Pope are credible.
"I believe they could try to kill him during one of his overseas trips or even in Rome. There are members of Isil who are not Arabs but Canadian, American, French, British, also Italians.
"Isil could engage any of these to commit a terrorist attack in Europe."
Pope Francis has spoken out about IS in the past, which has raised concerns that he could become a target.
But the Vatican has played down the warning, saying security officials are 'calm' ahead of the visit.
Vatican spokesman Father Federico Lombardi said: "There are no specific threats or risks that would change the Pope's behaviour or the way the trip is organised."