The garda chief has said no one underestimates how difficult it will be to bring the killers of Detective Garda Adrian Donohoe to justice.
Garda Commissioner Martin Callinan said steady progress was being made in the murder investigation, which he revealed would be slow and painstaking.
He maintained he was optimistic that those responsible would be brought before the courts.
"No one, including myself, is underestimating how difficult that process will be," said the commissioner. "But we have very good people working on the case. Very committed and dedicated people."
Thousands of gardai joined mourners at the funeral of the respected detective, who was killed as he confronted a gang of men on rural roads near his home on the Cooley peninsula near the border last Friday night.
Mr Callinan gave a reassurance that no stone will be left unturned in trying to bring Det Donohoe's killers to justice. The 41-year-old was shot in the head as he approached a five-man gang at a car in the grounds of his local credit union in the village of Lordship.
An 08-D navy Volkswagen Passat - stolen from Clogherhead in Co Louth on January 22 and used in the attack on Friday night - was later being found burnt out beside a forest in south Armagh.
"All of the resources that the state can deploy at the moment are being utilised in this investigation," said the commissioner. "All of the national units and all of the specialist units are assisting the local gardai, who are doing a tremendous job of work up there in pulling those details together."
The garda chief appealed for gardai and the PSNI to be given the space to catch the killers, adding that it would be dangerous for them to reveal information on suspects or investigation tactics.
Justice Minister Alan Shatter issued a fresh appeal for information. "There are husbands, wives, sons, daughters, neighbours, friends, who must know the individuals engaged in this," said Mr Shatter. "They are not five people operating in a vacuum."