He said he was “stunned by the absolute brutality” of the murder, one of many recent outrages “outside the normal” for terrorism.
Archbishop Martin said he was pleased by messages he had received from Islamic figures here and said the attack was something that “horrifies” every religion.
He said evil could only be combated with “goodness” and said education was the key to resolution.
His comments follow calls in France for tighter security for clerics, after Tuesday’s attack in Saint-Etienne-du-Rouvray, south of Rouen.
Fr Hamel, aged 86, was forced to his knees and had his throat slit by two knife-wielding attackers. They claimed links to Islamic State.
Speaking from the Catholic World Youth Day, in Poland, which was attended by Pope Francis, last night, Dr Martin said: “I think everyone is stunned by the absolute brutality of this.
“It’s very frightening to see the number of cases which go way outside the normal picture of terrorism, of individuals, in some cases known, in other cases not known, who carry out random, but very brutal, terrorist attempts.”
He toldthat he was concerned about similar attacks: “There is always a danger of copycat attempts and those copycat attempts will only be heightened the more you attract attention.”
Responding to the potential impact on Christian/Muslim relations here, he said: “We can thank God the relations between Muslims and Christians in Ireland are good. There is an understanding and that is actually improving day by day. I was pleased by some of the [contact] I got from some of the Islamic sources in Dublin, already some messages of sympathy. This is something no religion would stand over. It horrifies everyone.”
He said the only way of “combating this evil is by bringing a similar force of goodness into our society”.
He described as “not helpful” comments from US cardinal, Raymond Burke, that Islam wanted to rule the world and that the US should reassert its Christian roots.
“Does Islam want to rule the world?” said Dr Martin. “There may be some people of the Islamic faith who do, but Islam itself has another side within it, a caring and tolerant side.”
He added: “Longer-term solutions will come from education,” he said. “Education is the basis for real tolerance, and knowledge and respect for other religions, which is an extremely important thing.”
Shaykh Umar Al-Qadri, of the Islamic Centre Ireland, called on all the faithful to unite against terror and said he previously spoke about the persecution of Christians by “pseudo-Muslims”.
He said: “Radical Islam is an enemy to not just non-Muslims, but also to the Islam which was propagated by Prophet Muhammad.”