Gerry Adams, President of Sinn Fein, and John Hume, leader of the SDLP, held a secret 90-minute meeting on Saturday after what is believed to have been weeks of preparatory work by a group of Roman Catholic clergymen.
Neither side would discuss the content of the talks yesterday, but their timing is thought to be significant. They come only days after the IRA re-affirmed its commitment to armed struggle in its meeting with the peace campaigner Senator Gordon Wilson; just a month before local elections are due with Sinn Fein support dwindling; and at a time when moves are under way for the resumption of the Northern Ireland peace talks.
After Saturday's meeting in Londonderry, Mr Hume said that he hoped the talks would lead to a renunciation of violence but he added: 'This is only a hope.'
Speaking on BBC radio, Cardinal Daly praised Mr Hume. His party will be in direct competition with Sinn Fein for the nationalist vote next month.
Cardinal Daly said: 'I greatly admire the courage of John Hume in continuing with his work for peace and being prepared to take political risks - quite considerable physical risks - in doing what he's doing.
'I sincerely hope, and thousands hope with me, that it may lead to an end of violence and to peace.'
Kevin McNamara, Labour's spokesman on Northern Ireland, and Peter Temple-Morris, the Conservative co-chairman of the British-Irish Parliamentary Body, welcomed the talks. Each said that they had complete faith in Mr Hume's ability to negotiate with Sinn Fein, but they felt progress would be achieved only over the long term.
Sinn Fein and the SDLP held a series of meetings in the late 1980s, which broke down after they failed to reach agreement on even basic issues. The SDLP argued that British involvement in Northern Ireland was no longer colonial and had moved to a position of neutrality; Sinn Fein considered it an occupation.
Their differences after each meeting were published and widely circulated during that series of talks. Their decision now to keep the contents of meetings secret is a good sign, according to Mr Temple-Morris. 'For Sinn Fein to agree to silence suggests that it is not feeling in a strong position,' he said. 'It has been notoriously weak in getting public backing, so its involvement in the resumption of talks on a private, low-key basis augurs well for a degree of success.'
Sinn Fein chairman Tom Hartley, Mr McNamara and Mr Temple-Morris yesterday rejected a call for the return of internment made by Senator Wilson, whose daughter, Marie, was killed in the 1987 Remembrance Day bombing at Enniskillen.
Mr Wilson, who was devastated when the IRA rejected his peace overtures last week, said in an interview with the Sunday Times that he believed internment was the only alternative to terrorism.
The three said that they respected Senator Wilson's peace efforts but one said the call for internment 'came more from a grieving father than an Irish senator'.
Pearse McCauley, the suspected IRA terrorist, appeared before Dublin's anti-terrorist Special Criminal Court on four firearms charges. Mr McCauley, 28, of Strabane, Co Tyrone, Northern Ireland, who was arrested at Connolly station, Dublin, on Friday, was remanded in custody and will next appear in court on 21 April.