The attempt is to be made after next month's local council elections, with the Government moving away from its previous stance as facilitator into a new phase in which its own preferences are made clearer.
John Major declared: 'One thing is certain - the people of Northern Ireland do not want another 23 years like the last 23 years.'
He went on: 'There is a great feeling right across the community that people want a settlement. They want peace and they want an end to the murders.'
Some local politicians responded positively to the new approach, although an instant indication of the difficulties came from the Rev Ian Paisley, leader of the Democratic Unionist Party, who called Mr Major a hypocrite.
Mr Paisley said that he would not take part in talks until Articles 2 and 3 of the Irish constitution (claiming jurisdiction over Northern Ireland) were dropped, declaring: 'I will not be getting round the table until the Anglo-Irish agreement is suspended and Articles 2 and 3 are gone.'
A heavy schedule took the Prime Minister, who arrived in Northern Ireland on Tuesday night, to a variety of engagements, which included meetings with businessmen, industrialists, soldiers and policemen.
In Strabane, Co Tyrone, he opened a new Royal Ulster Constabulary station which, because of its heavy security defences, has cost almost pounds 11m to build.
Mr Major's message to the local politicians was that no more time should be lost before negotiations resume, following their unsuccessful ending last November. He implicitly criticised them for an alleged lack of appetite for new discussions, declaring: 'We want the talks to start as soon as possible. I think many people underestimate the progress that has actually been made in the talks.
'Many people would have said it can't be done, but it has been done and it has been done because of the talks and because of the pressure and the feeling of the people of Northern Ireland. We must press ahead. There are grounds for hope.'
Mr Major said that Northern Ireland would remain part of the United Kingdom as long as the majority of people there wanted it. On the talks, he warned that the participants must be prepared to move away from entrenched positions and show greater flexibility.
In a reference to recent speeches by Dick Spring, the Irish Minister for Foreign Affairs, the Prime Minister said that he had been encouraged by his comments on Articles 2 and 3.
Overall, however, Unionists may take more comfort from his words yesterday, inferring from Mr Major's remarks that the Government may be seeking greater concessions from the nationalist side than from Unionists.
The lack of progress in previous rounds of talks have left few optimistic that new talks are likely to succeed. The most immediate problem will be to persuade Mr Paisley to drop his bald assertion that Articles 2 and 3 must go before he will talk again.
After that will come the task, which most observers agree will be one of momentous proportions, to somehow find a way of reconciling the Unionist and nationalist viewpoints.
Previous talks demonstrated all too plainly the fundamental differences in approach here, for Unionists were concerned with strengthening the link with Britain, while nationalists sought to dilute the authority of Britain by bringing in new Irish and European commissioners.
The Taoiseach, Albert Reynolds, said in Dublin yesterday that he shared the aim of reopening talks. He added: 'You can take it we will be involved in any initiative, ideas or proposals on the north. There are no differences between the Irish and British governments, and I have no doubt there will be full consultation.'Reuse content