Sinn Féin's chief negotiator Martin McGuinness has said he hopes the IRA will respond positively to Gerry Adams's call for the organisation to embrace purely political and democratic activity.
He said the IRA leadership had initiated an internal debate and they awaited the conclusion of those discussions.
"I have no intention today of commenting on this internal discussion. That is a matter for the IRA and, as Gerry Adams has repeatedly said, that organisation should be given the space to thoroughly debate these matters."
It was clear that a positive response from the IRA would have an immediate and enormous impact on on the political situation, he said.
"It would give a much-needed new momentum to the peace process, deal with genuine unionist concerns, remove from the leadership of unionism its excuse for non-engagement, and it would put enormous pressure on the DUP to come on board the peace process for the first time."
Of course, said Mr McGuinness, the DUP might not choose to do so.
"Their current political position gives little cause for optimism. Their political role over the three decades of their existence has been singularly negative and divisive. But despite all this, Sinn Féin is prepared to engage with the DUP, because non-engagement is not an option.
"Refusing to talk to one's opponents is a failure of politics, a failure of political leadership and creates conditions in which conflict can occur."
Sinn Féin recognised and accepted the DUP's electoral mandate, he said. "We disagree with them fundamentally, but we are prepared to do political business with them just as much as they must do business with Sinn Féin because we have an electoral mandate, because we are the largest nationalist party in the North, the largest pro-agreement party in the North, and the third largest party on the island of Ireland."
He told the MacGill Summer School that at some point the DUP would have to enter the world of political dialogue, compromise and agreement.
"The days of second-class citizenship, of unionist domination, of the one-party state are gone forever."
DUP chairman Maurice Morrow said that in the Republic politics had not been placed on hold until Sinn Féin was fit to take its place in government, yet people were being held to ransom in Northern Ireland.
"Why should we be asked to wait? There has never been a satisfactory answer to why we should be asked to have Sinn Féin in government in Northern Ireland, but yet we are told they are unfit to be in office in the South."
Mr Morrow said there was no question of unionists accepting in the North what nationalists would not accept in the South.
"Before anyone from the Republic of Ireland asks us to consider Sinn Féin for government in Northern Ireland, let them first tell us that they would permit them in their administration."
Direct rule, he said, meant that Sinn Féin was not in government in Northern Ireland, but it was not a panacea to their problems.
"We should not confuse what is the better of two unpalatable solutions with what is best for the province. Direct rule does not deliver what we would like to see in Northern Ireland and undoubtedly does not provide for the best form of government here."
He said there was a challenge for everybody to keep up the work, but there was also a challenge to the government to ensure that those who used or threatened violence were not allowed to dictate the pace of politics in Northern Ireland. "Why should the inability of Sinn Féin to give up criminality and paramilitarism hold back the rest of us?"
SDLP leader Mark Durkan said that the drift would continue if direct rule continued, not just the drift into political failure, but also the drift of communities away from each other.
"Equally, if we have a government dominated by Sinn Féin and the DUP, and from which other parties like ourselves can be automatically excluded, as last December's deal proposed, we risk failure."