The Northern Secretary is expected to announce today whether the Assembly will be recalled for fresh elections for the office of First Minister and Deputy First Minister.
Speaking last night outside the Northern Ireland Office, where members of the pro-agreement parties had been having round-table discussions, Dr John Reid said "substantial and rapid progress" had been made.
"Obviously, this morning's events in the Assembly were a setback, because, despite winning over 70 per cent of the votes, the First and Deputy First Minister could not be elected", he said.
"Our aim is to get to the point soon where we can have a successful resolution of the elections for First Minister and Deputy First Minister. I think there are grounds for believing that we can create the political context in which a successful election can take place. I can't be sure of that . . . but I think we are making rapid and substantial progress in that direction."
Dr Reid said he would continue to talk to the pro-agreement parties last night and hoped to be able to make a further statement today.
"I believe we all need to do whatever is necessary to move this process forward, because people are fed up with delay. They are fed up with lurching from crisis to crisis."
Dr Reid was asked if the redesignation of parties from "Other" to "Unionist" undermined the credibility of the political institutions.
"I think what undermines people's belief in the process as a whole is constant interruptions, whether that be for suspensions, or for elections, or for walkouts, or for people having rotating ministries", he said.
"People in Northern Ireland have been endlessly patient in waiting to see what they have voted for, which is stable, sustained institutions composed of politicians elected in Northern Ireland making decisions in Northern Ireland."
Earlier, the leader of the Alliance Party, Mr David Ford, expressed dissatisfaction with the voting system of parallel consent, which effectively denied the five members of his party a say in the election of First and Deputy First Ministers.
"The people who voted for us are not being represented on the same democratic basis as the people who voted for other people", he said.
Mr Ford said it was clear that the voting system in the Assembly had to be changed. "That's something that will not be put right in the next few hours but will require legislation.
"We want rid of designations. We believe people in Northern Ireland want to see the back of designations."
Mr Ford confirmed that the British Prime Minister had spoken to him by phone yesterday morning, but he would not say what was discussed.
The executive of the Alliance Party met last night to discuss the party's earlier meeting with Dr Reid.
The leader of the Women's Coalition, Prof Monica McWilliams, said she was sorry the Assembly had been unable to elect a First and Deputy First Minister.
"We have done everything in our power to make our votes count. Others have used their votes to perpetuate the crisis at the heart of politics and to further instability. There are clear flaws in the voting system, though we recognise the importance of the cross-community safeguard."