The Sinn Fein president, Mr Gerry Adams, emerged from yesterday's hour-long meeting at No 10 Downing Street with the British Prime Minister, Mr Tony Blair, declaring it "a good moment in history".
Both sides agreed they had "engaged" on the issues central to the search for a political settlement in Northern Ireland, although neither retreated from established positions - Mr Blair on the principle of consent, Mr Adams on the goal of Irish unity.
Mr Blair and the Taoiseach, Mr Ahern, are to review developments in the multi-party talks process later today in the margins of the EU summit in Luxembourg. However, despite their mutual relief that yesterday's meeting proved "positive and constructive", the two leaders face what one source last night described as "a Sinn Fein/Ulster Unionist stand-off" in the Stormont talks.
It now seems clear that Mr Blair had hoped to secure assent on likely "heads of agreement" in the talks process ahead of yesterday's meeting with Sinn Fein. And there is some uncertainty in London and Dublin about the implications of Sinn Fein's refusal earlier this week to approve a paper incorporating reference to a Northern Ireland assembly.
The assumption is that Sinn Fein's position is tactical and that the party is reserving its position on matters relating to the internal government of the North until the Strand Two North/South dimension takes shape.
However, Mr Blair and Mr Ahern will be anxious about the bitter aftermath of yesterday's meeting which saw the Ulster Unionists reject Mr Martin McGuinness's suggestion that "the next important development" should be a meeting between Mr Adams and the UUP leader, Mr David Trimble, and about the serious possibility that the talks process might adjourn for Christmas with agreement limited to the procedures for its resumption in the new year.
At the end of a historic day which saw the first talks between a British prime minister and republican leaders in Downing Street for 76 years Mr Adams said that, contrary to the "media image", he found a Prime Minister who engaged and listened. He had had "a real sense of exploring each other's analysis".
Mr Adams said: "I think for the first time in my lifetime a British prime minister was able to hear from an Irish republican that the relationship between our two islands, which has meant so much suffering and death and pain and agony, can be put to one side, can become part of our history and that Mr Blair is significantly placed to be the British Prime Minister who brings about a new history, a new relationship between the people of these islands."
He stressed Sinn Fein's view that "the hurt and grief and division which has come from British involvement in our affairs must end". And he repeated his theme that the multi-party talks were a phase in a process in which his party remained "absolutely committed to bringing about the goal of an Ireland free and united, where all the people on this island can live together in peace and harmony . . ."
Facing Mr Adams directly across the cabinet table, Mr Blair said he was committed to the principles of consent and he was not "a persuader for Irish unity". He "went out of his way" to praise Mr Trimble's constructive role in the talks process and said the reality was that there would be no process without Ulster Unionist participation.
Mr Blair also told Mr Adams and his six colleagues it was important that he could "look you in the eye and hear you say: `We remain committed to peaceful means' because if there is any going back to violence we will have wasted the best opportunity for peace in a generation".
Mr Blair said: "This is a choice of history: violence and despair or peace and progress."