The Northern Secretary, Mr Mandelson, has once again firmly ruled out giving a dual name to the new Northern Ireland police service, though it would be "politically attractive" to do so.
He was speaking in Canada. The policing issue also featured in talks in Washington, where the Minister for Foreign Affairs, Mr Cowen, visited the White House.
Mr Mandelson said he did not believe a dual name would be good for the police, and for operational purposes the service would be known as the Police Service of Northern Ireland.
"As I made clear in the House of Commons, I intend that name - and that name alone - to be used in all the police's dealings with the public," Mr Mandelson said in an address to the National Research Council of Canada.
Mr Mandelson said he was determined that the new Police Service of Northern Ireland, incorporating the RUC, will mark a "radical new beginning as the Patten report intended".
To be fully effective, a police service must reflect the community it polices. Only then can it truly police the community by consent, he said.
"That is why the religious composition of the police must change and why the Government has a settled view that the exceptional 50/50 selection procedure will be implemented, starting next April."
Mr Mandelson said the new police service needed to be truly supported by both unionists and nationalists. He said he hoped when the first new recruits completed their training community and political leaders on all sides would applaud them.
"Failure to do so would be to risk letting slip from our grasp the key reforms of the Good Friday agreement."
Mr Mandelson said paramilitarism was still a reality in both communities and was "deeply corrosive". "It is violent, intolerant, oppressive and exploitative," he said.
We must be careful, he added, that as politics is restored to its rightful place a rump of paramilitarism does not stay behind like "a grumbling infection in the body politic, a Mafia-like virus in society."
In relation to marching, Mr Mandelson said the summer had once again been disfigured by confrontations. "Northern Ireland is escaping the pictures of bombings and shootings which defined it in the eyes of the world. Are we now going to let Northern Ireland be known instead for ugly standoffs, barricades and disorder flowing from marches?" he asked.
In Washington the Minister for Foreign Affairs, Mr Cowen, briefed the White House, senior members of Congress and the State Department on the situation in Northern Ireland and lobbied for US support for Ireland's bid for a seat on the UN Security Council.
After his meeting with Mr Sandy Berger, President Clinton's national security adviser, Mr Cowen said he had updated him on the Government's position on the ongoing discussions on implementing the reform of the RUC.
He said the aim was "a consensual police service which will have the allegiance of both sides of the community and, very importantly, will allow for a fuller participation by members of the nationalist community in the police service of the future".
The Minister said the result they wanted was "a win-win situation for everyone in Northern Ireland." There was a need for full allegiance to be given to a consensual police service which will attract a representative balance in time in terms of its recruitment processes, and have a full accountability mechanism which is transparent."
Asked how the US could play a role in this, Mr Cowen said the Clinton administration "will be speaking to all sides - the governments and the parties - encouraging us to work further and to come up with solutions which will meet the requirements of the situation". The US has been "generally supportive of the process we are engaged in".
Asked if the US favoured "full implementation" of the Patten recommendations for RUC reform, Mr Cowen said: "The US wants to see full implementation of the Good Friday agreement and is supportive of the agreement."