"Whoever makes this choice, profanes Christian martyrdom," said Chaldean Catholic Patriarch Louis Sako of Baghdad, warning that responding with hatred or increased suspicion is "sacrilegious blasphemy" of the priest's death.

"These people betray and disrespect Father Jacques more than those who inspired their killers," he told the Vatican Insider two days after the 85-year-old priest was killed during Mass in St.-Etienne-du-Rouvray. The attackers, who slit the priest's throat, claimed allegiance to the Islamic State and the group later claimed responsibility for the priest's murder.

Paris Cardinal Andre Vingt-Trois' immediate reaction to the attack was to urge Catholics to "overcome hatred that comes in their heart" and not to "enter the game" of the Islamic State that "wants to set children of the same family in opposition to each other."

Boston Cardinal Sean P. O'Malley echoed that sentiment nearly a week later, telling reporters at World Youth Day in Krakow, Poland, that it is a great danger to demonize Islam after such an attack. "We are talking here about fanatic terrorists who are persecuting Christians and we have to be very clear we are not painting everyone with the same brush," he said.

Pope Francis also made that distinction in speaking to reporters on the plane to and from World Youth Day events. On the flight to Poland, a day after the priest's death, the Pope stressed that the world is at war but religions are not. Four days later, on the return flight, he said that even though the priest's murder was committed in the name of Islam, it is unfair to label an entire religion as violent because of the actions of a few fundamentalists.

Basilian Father Thomas Rosica, CEO of Canada's Salt and Light Catholic Media Foundation, likewise stressed in a July 27 Facebook post: "ISIS is not Islam. ISIS and any form of terrorism in the name of God is an aberration of religion."

Father Rosica, who also is the English-language assistant to the Holy See Press Office, said: "We must distinguish between true religion and the twisted religion used to justify hatred and violence." He also stressed the need "now more than ever" for Christian-Muslim dialogue.

Muslim and political leaders similarly called out the Islamic State for its ploy to provoke religious hostilities. France's Prime Minister Manuel Valls said Islamic State militants aimed to "attack one religion to provoke a war of religion."

The Council on American-Islamic Relations, the nation's largest Muslim civil rights and advocacy organization, condemned the attack and also said the "apparent goal of the cowardly murderers is to create divisions between faiths and to breed hostility between the followers of different faiths. We must not allow the terrorists to achieve their twisted goal."

But messages not to give in to hate competed against the vitriolic din on social media linking Muslims and immigrants as a group to the act of terror in France and other recent terrorist attacks.

"Attacks like what we saw in Rouen have the potential to harm relations between Christians and Muslims. But so do our own responses," said Jordan Denari Duffner, a research fellow at Georgetown University's Bridge Initiative studying Islamophobia.

Duffner, in a July 28 email to Catholic News Service, said she has been "disappointed by a number of comments made by Catholics, even clergy, on social media who are reacting to this tragedy in a way that blames Muslims and their religion and that seems to sow more division than bonds."

"As Catholics, our response to Father Jacques' murder in Normandy must be to open our arms wider to our Muslim brothers and sisters," she said, adding that the priest, who was friends with the town's imam, would want that.

She also said Christians should "stop calling on Muslims to condemn these murders and attacks" because they have already been doing so. She also noted that the "vast majority of Muslims have no more to do with terrorist groups than Christians do."

Duffner said the negative reactions against Islam after the priest's death reminded her of the opposite reaction taken by Trappist Father Christian-Marie de Cherge, one of seven monks slain by Islamic terrorists in Algeria in 1996. A group of Islamic terrorists announced they had "slit the throats" of the monks after they kidnapped them from their monastery and held them hostage for two months.

In a letter the priest wrote, anticipating that he would be killed, he said: "I do not see, in fact, how I could rejoice if this people I love were to be accused indiscriminately of my murder.”