Anyone with information about the murder of Paul Quinn at the weekend has a "duty before God" to pass it to the Garda or PSNI, the Catholic primate has said.
Archbishop Seán Brady said the killing was brutal, evil, inexcusable and atrocious.
Calling for what he called the "tyranny of violence and intimidation" to be defeated, he urged that there be no reprisals.
Mr Quinn (21) was lured to farm buildings at Tullycoora on the Castleblaney to Newtownhamilton road on Saturday. There he was severely beaten by a group of people. He died a short time afterwards in Drogheda hospital. His family has blamed the Provisional IRA, a claim denied by Sinn Féin.
"The brutal murder of Paul Quinn has shocked and appalled a whole community. I offer my sympathy to his grieving parents and family," Archbishop Brady said in a statement yesterday.
"This barbaric deed should be seen for what it is - evil and inexcusable, causing revulsion and shame in all right-minded people. It shows a total lack of respect for the God-given gift of human life," he said.
"I hope that those who carried out this atrocious crime will soon be apprehended and brought to justice. Those with information have a duty before God to pass it on to the gardaí or PSNI. The tyranny of violence and intimidation must be defeated."
He said the Quinn family has pleaded that there should be no reprisal for the killing. "I appeal for that call to be totally respected." His appeal was followed by a call by Deputy First Minister Martin McGuinness for anyone with "a scintilla of evidence" to go to the police.
"The people who murdered Paul Quinn are criminals," he said. "They need to be arrested and there is a duty and a responsibility with everyone with any scintilla of information whatsoever to bring that information forward to both the Garda and the police here in the North." His office confirmed that Mr McGuinness had spoken to both Minister for Foreign Affairs Minister Dermot Ahern and prime minister Gordon Brown by telephone concerning the murder.
It is understood the postmortem on the victim's body continued yesterday and that his funeral is planned for his home village of Cullyhanna, Co Armagh tomorrow morning.
The family has claimed Quinn was defying an "exiling" order from local republicans and that this cost him his life.
There was no indication yesterday of any fresh threat to the stability of the powersharing Executive.