The negotiations, if successful, could end with Britain setting a mid-November election date in Northern Ireland. The vote, which Blair postponed in May, would fill a 108-seat legislature — the bedrock for any revived Catholic-Protestant administration in the province.
This week's talks include Gerry Adams, leader of Sinn Fein, the party linked to the Irish Republican Army; and Ulster Unionist Party chief David Trimble, who angered many of his fellow British Protestants in 1999 by forming an administration alongside Sinn Fein.
Blair told reporters at midday the climate of the talks was "conducive to finding a way forward."
"The omens are very, very good if we can find the right way of having an election in a positive and constructive atmosphere," Blair said.
Ahern added that some issues were unresolved, but all parties "want to see these resolutions found."
Trimble said he was "hopeful," but added any agreement would require the IRA to end all activity and "deal effectively" with disarmament.
"We would like to make progress on these matters, because we think that people in Northern Ireland would like to see the assembly back and the assembly at work," Trimble said.
Adams said the negotiations were "a collective endeavor, a collective effort. We will do our best."
The U.S. envoy to Northern Ireland, Richard Haass, canceled planned engagements in Belfast to take part in the London talks.
Northern Ireland's administration — which included a moderate Catholic party and an extremist Protestant party — suffered repeated crises and fell apart 12 months ago after police uncovered evidence of Sinn Fein involvement in an IRA spying operation inside the government.
The Ulster Unionists say they won't revive any coalition involving Sinn Fein unless the IRA promises to cease all activities — including training, gathering intelligence on potential targets, and attacking criminal opponents — and disarm. Sinn Fein insists it won't deliver any IRA commitments unless Britain sets and sticks to a new election date.
Both sides do agree that Britain should decide this week whether to hold the election next month. Trimble said he expects an announcement by Wednesday.
Opinion polls and electoral trends in Northern Ireland suggest that Sinn Fein could surge ahead of its moderate Catholic rivals, the Social Democratic and Labor Party, while Ian Paisley's uncompromising Democratic Unionist Party could seize a majority of Protestant votes from the Ulster Unionists.
Analysts agree such an outcome — with hard-liners on both sides in command of opposite sides of the legislature — would make the revival of any power-sharing administration much more difficult.
By Ed Johnson