The priest was killed in front of the Church of the Holy Spirit after saying Sunday Mass.
According to Reuters, police said that gunmen stopped the priest's car, dragged him and the deacons out and shot them. Iraqi sources said militants related to al-Qaida are responsible for the increasing persecution of Christians in Mosul.
The papal telegram was sent to Chaldean Archbishop Paulos Faraj Rahho of Mosul.
The telegram said: "The Holy Father was deeply saddened to learn of the senseless killing of Father Ragheed Aziz Ganni and subdeacons Basman Yousef Daoud, Ghasan Bidawid and Wadid Hanna, and he asks you kindly to convey to their families his heartfelt condolences."
It continued: "He willingly joins the Christian community in Mosul in commending their souls to the infinite mercy of God, our loving Father, and in giving thanks for their selfless witness to the Gospel.
"At the same time he prays that their costly sacrifice will inspire in the hearts of all men and women of good will a renewed resolve to reject the ways of hatred and violence, to conquer evil with good and to cooperate in hastening the dawn of reconciliation, justice and peace in Iraq."
The telegram concluded: "To the families and to all who mourn their dead in faith and in the hope which draws its certainty from the resurrection, His Holiness cordially imparts his apostolic blessing as a pledge of consolation and strength in the Lord."
Meanwhile, the Chaldean patriarch of Babylon, Emmanuel III Delly, published a declaration regarding the killings.
"With hearts full of bitterness the patriarch of Babylon for the Chaldeans, His Beatitude Mar Emmanuel III Delly, and all the Chaldean bishops raise a disdainful protest and denounce the martyrdom" of the four clerics, the declaration said.
It continued: "This is a shameful crime that any person of conscience rejects. Those who committed it did a horrendous thing against God and humanity, against their brothers who were faithful and peaceful citizens besides being men of religion who always offered their prayers and their supplications up to Almighty God that he would bring peace, security, and stability to all of Iraq."
The note said that the Chaldean bishops of Iraq, who are meeting in a synod in al Qosh, offered their condolences and prayers.
"The bishops ask everyone for unity and solidarity in these difficult moments, and on this sad occasion, they repeat what they have already declared before about the persecution of Iraqi Christians, their forced emigration, and their being pushed to deny their faith," the declaration concluded. "They ask the Iraqi leaders and the international organizations to intervene and take the necessary steps to put an end to these criminal acts."