Detective Garda Adrian Donohoe, a father of three in his 40s, died after sustaining fatal gunshot wounds at the Lordship Credit Union in Bellurgan, Jenkinstown, where a botched robbery took place at around 9.30pm on Friday.
He was escorting a cash delivery to the premises on the Cooley Road with a colleague, who was left traumatised but unhurt after the shooting.
Several shots were fired by the gang of robbers, who were waiting outside, when the detective approached them.
Gardaí said Mr Donohoe, originally from Co Cavan but stationed at Dundalk, was shot without warning and had not drawn his weapon.
A massive cross-border hunt has been launched to catch the killers.
Investigations are underway into whether elements such as dissident republicans were involved, or whether a criminal gang was responsible.
Specialist officers from the Garda Forensic and Technical Bureau are conducting examinations, and it is believed the police force is now hunting four men in a grey Volkswagen Passat which fled the scene.
Those who perpetrated such a cowardly attack cannot be allowed to escape justice. Those who would terrorise communities must not be able to evade justice
Peter Robinson and Martin McGuinness
Tributes have flooded in for Adrian Donohoe, who was well-known in the area and whose death has left the local community in shock.
His colleagues described him as dedicated, diligent and hugely popular.
Garda Commissioner Martin Callinan said: "He was a very popular member of An Garda Siochana, a very efficient member, someone who was revered both by his peers and members of the community where he served."
PSNI Chief Constable Matt Baggott spoke to the commissioner on Saturday and has offered every assistance and support for the investigation.
A PSNI statement said: "He also asked that his condolences and those of the PSNI be passed to Detective Garda Donohoe's family and colleagues."
A book of condolence has been opened at the garda station in Dundalk, where police and members of the public have left flowers and messages for the Donohoe family.
Irish President Michael D Higgins described the killing as a dreadful crime and said all Irish people would be truly appalled.
Taoiseach Enda Kenny said: "(It) has left a family without a husband and father and the Garda Siochana without a brave and valued member."
A joint statement from the Office of the First and deputy First Ministers offered "our sincere and heartfelt sympathies to his family, friends and colleagues".
Mr Robinson and Mr McGuinness added: "We must all work together on both sides of the border to make sure they are caught for this murderous deed."
Sinn Féin president and Louth TD Gerry Adams said: "I am shocked at this crime.
"I extend my deepest sympathies to his family and colleagues and appeal to those with information about this crime to co-operate with the Gardaí."
On behalf of the Government and of the people I would like to express my condolences to Adrian's wife and children and to all his extended family at this unbearably sad time.
Taoiseach Enda Kenny
TD Alan Shatter, the Irish minister for justice, equality and defence, said: "The Irish people rightly have great respect and admiration for members of An Garda Siochana and the work they do in protecting the community. They will share my revulsion and horror that a Garda has so tragically lost his life in the course of his duties."
Stormont Justice Minister David Ford said: "I condemn this brutal murder of Garda Donohoe and offer my deepest sympathies to his family and fellow Garda officers.
"I have spoken to Justice Minister Alan Shatter and reinforced my commitment for both jurisdictions to work together against criminal gangs and protect our communities."
Secretary of State for NI, Theresa Villiers, said: "I was shocked to hear of the appalling murder of Detective Garda Donohoe.
"It was a senseless and cowardly act and all right thinking people will be revulsed by it. I send my sincere condolences to his bereaved family and colleagues."
Ulster Unionist Policing Board Member, Ross Hussey MLA, said: "I was sickened to hear of the murder of Detective Garda Adrian Donohoe.
"On behalf of my party and many others, I wish to extend my heartfelt sympathies to his family, friends and all members of An Garda Siochana."
SDLP Policing spokesperson Conall McDevitt said: "People across the Island will be united in condemning this appalling crime and outraged that Mr Donohoe was killed while attending a reported robbery and without drawing his weapon."
"This news will hit PSNI officers hard too as there is a great sense of comradeship amongst police officers and their families in Ireland and indeed between Britain and Ireland."
Detective Garda Donohoe was the first garda officer to be killed in 17 years.
Detective garda Gerry McCabe was also on escort duty when he was shot dead at a post office in Co Limerick in 1996. His widow Anne said: "I have to sympathise with the family and the shock they are going through."
Paul Breen, a member of St Patrick's GAA club, said: "The whole community is shocked - what else could they be? But, for these people, this is just a way of life."
A full post-mortem examination was to take place in Drogheda on Saturday, Gardaí said.