PSNI Chief Constable Sir Hugh Orde met Garda Commissioner Fachtna Murphy
Police chiefs from Northern Ireland and the Republic have met in Belfast.
The talks followed the murders of two soldiers and a policeman by dissident republicans in the last week.
Assessing the security threat posed by the dissidents, PSNI Chief Constable Sir Hugh Orde said the two forces were working together.
"The relationship is excellent. We are determined to bring those responsible for the despicable murders over the last week to justice," he said.
An Garda Siochána Commissioner Fachtna Murphy said an attack on a police officer was an "attack on the whole of society".
Sappers Mark Quinsey, 23, from Birmingham, and Patrick Azimkar, 21, from London, were shot by the dissident republican Real IRA as they accepted a pizza delivery on Saturday.
Constable Stephen Paul Carroll was murdered in Craigavon, County Armagh, on Monday. The murder was claimed by the dissident republican Continuity IRA.
Commissioner Murphy said co-operation between both police forces have been "growing steadily and surely over recent years".
"I spoke with Sir Hugh on Monday evening when I received the news about Constable Carroll to express my condolences to both the family and the Police Service and to assure him of our continued support in tackling and frustrating this small group of criminals," he said.
These are dangerous groups, they are very much small in number, but they are very keen to increase their influence
Chief Inspector Chris Yates
Sinn Féin President Gerry Adams and Taoiseach Brian Cowen have been meeting in Dublin to discuss the security threat.
Speaking afterwards, Mr Adams said the dissident groups should be given no breathing space.
"No-one should support them, give succour to them, join them, or work with them," he said.
A spokeswoman for Mr Cowen said he and Minister for Foreign Affairs Micheal Martin were "heartened by the united response to the attacks".
She said they were "determined to press ahead with the development of the democratic political institutions in Northern Ireland, including through the forthcoming devolution of policing and justice powers to the Northern Ireland Executive".
Meanwhile, the police commander in Londonderry has warned that dissident republicans are on a recruitment drive in the city.
The men were killed over a period of 48 hours
Chief Inspector Chris Yates said: "These are dangerous groups, they are very much small in number, but they are very keen to increase their influence.
"The reality is they are out there in the communities, working, trying to recruit people, trying to pervert people, trying to turn people to their cause and that's very worrying."
He said the PSNI would be maintaining a high profile to prevent attacks.
A Sinn Féin delegation is to attend the funeral on Friday of Constable Carroll in Banbridge.
The delegation will include Sinn Féin policing board member Alex Maskey, MLA John O'Dowd who represents Upper Bann, and Banbridge councillor Dessie Ward.
Meanwhile, a service has been held at Massereene Barracks in Antrim for the two soldiers who were killed on Saturday.
Four men, including two pizza delivery men, were injured in the Antrim attack. One of them remains in a critical condition and another is seriously ill.
The partner of one of the delivery men has described the attack as a "terrible, violent act" and extended her sympathy to the families of the murdered soldiers.
She also praised medical staff for saving her partner's life.
Children attended the vigil in Craigavon
"We would like to thank the medical staff at Antrim Area Hospital for all the care and attention given to my partner," she said in a statement.
Thousands of people attended peace rallies across Northern Ireland on Wednesday following the murders .
Silent protests took place in Belfast, Lisburn, Newry, Downpatrick and Londonderry.
A peace vigil was also held in Craigavon near the site where Constable Carroll was shot.
On Thursday, police were granted a further five days to question two men, aged 17 and 37, about the murder.