The pontiff had expressed a wish to visit the country's displaced Christians but the Vatican said it was not possible.
Louis Raphael I Sako said: "I don't know why the Holy See is so concerned. I can give an assurance that nothing would happen to the Pope. His security would be guaranteed 100 percent."
He also said having Pope Francis visit would have "high pastoral and spiritual symbolism".
The Muslim extremist group Islamic State has captured large parts of northern Iraq, and persecuted tens of thousands of Christians and other religious minorities.
Before 2003, there were 1.2 million Christians in Iraq. But persecution from Islamic State has caused this number to fall to approximately 350,000 today.
Islamic State has also made direct threats to the Vatican, saying: "We will conquer your Rome, break your crosses, and enslave your women."
In an interview with Aid to the Church in Need the Patriarch called for ground troops to drive Islamic State out of the northern city of Mosul, and nearby Nineveh.
"We don't know when the villages of the Nineveh plains will be liberated. I think it will take some time. The coalition forces haven't decided yet.
"OK, they are conducting air strikes. But we need ground troops to push ISIS back.
"This is hitting us very hard because it's the well-educated Christians who are leaving."
Patriarch Sako said he'd contacted the Holy Father personally to invite him to Iraq, and given him a prospective itinerary for the Papal visit.
Baghdad is currently under recurring attacks from Islamic State.