The Secretary of State for Northern Ireland, Mr Paul Murphy, branded paramilitarism "redundant" follwing his meeting with the Minister for Justice Mr Michael McDowell in Dublin this afternoon.
"Paramiltarism is a thing of the past. We are working to ensure that their is no safe haven for criminals anywhere," he stated.
The two sides held a two hour meeting at which they discussed planned anti-terrorism legislation to crack down on dissident republican groups in particular, but also on loyalist groups and the wider international terrorist threat.
Echoing the Northern Ireland Secretary's comments, Mr McDowell stated that a programme of legislation was forthcoming in the Republic.
"Further measures necessary for North-South security, eliminating any loopholes, will emerge. There will be operational implications for both police forces," he said.
"We have planned a useful programme of work with a wide agenda for intensive co-operation between the forces North and South," he added.
A key aspect of the new leglislation will focus on the activities of dissident republican groups, the the "Real IRA" and the Continuity IRA, to offset those groups' continued attempts to undermine the peace process.
Both governments are anxious that any dramatic demilitarisation may leave border areas open to terrorist attack, undermining any new attempt to reactivate the Stormont institutions.
"We need to tackle the essential issue of paramilitary activity, to make the institutions (of government) stable," Mr Murphy asserted.
"We will achieve the amount of security necessary to ensure that the Good Friday Agreement succeeds," Mr McDowell added.
The leglisation will also cover the activities of dissident loyalism and organised cross-border crime, as well as the potential threat from international terror groups as al-Qaeda.
The Garda Commissioner, Mr Pat Byrne, and the PSNI Chief Constable, Mr Hugh Orde, also attended this afternoon's meeting.
Following the meeting, one of a series of bilateral discussions between the governments, the Secretary of State proceeded to Iveagh House to meet with the Minister for Foreign Affairs, Mr Cowen.
Soon after the meeting, SDLP leader and former Deputy First Minister, Mr Mark Durkan emerged from Iveagh House where a party delegation, including SDLP deputy leader Mrs Bríd Rodgers, Mr Alex Attwood and Mr Sean Farren, met with the Mr Cowen.
The group then moved to Government Buildings for talks with the Taoiseach.
Mr Durkan met Sinn Féin party president Mr Gerry Adams at Stormont this morning.
Further talks in London and Belfast over the next week will include a meeting between the Taoiseach, Mr Ahern, and the British Prime Minister, Mr Tony Blair, in Downing Street on Thursday.
Hillsborough will be the scene of a summit between the two leaders and members of the pro-Agreement parties on Monday.
They will be seeking to secure a deal between the IRA and the British government thought to involve a decommissioning move in exchange for a package of measures covering policing and scaling down of the British Army presence in the North.
However, Sinn Féin have denied reports that such a deal is imminent.