DUP leader Ian Paisley has said that if all his conditions are fulfilled he will accept the first minister's post after a spring election.
Ian Paisley has said he will accept the first minister's post
The DUP leader released his statement after confusion about exactly what occurred in Stormont on Friday morning.
In his speech, Mr Paisley said the circumstances had not been reached where there could be a nomination or designation by his party.
Other parties said that the DUP position needed to be clarified.
Sinn Fein nominated Martin McGuinness as deputy first minister.
Mr Paisley said in the assembly chamber: "There can only be an agreement involving Sinn Fein when there has been delivery by the republican movement, tested and proved over a credible period in terms of support for the PSNI (the police), the courts, the rule of law, a complete end to paramilitary and criminal activity and the removal of terrorist structures.
"Clearly, as Sinn Fein is not yet ready to take the decisive step forward on policing, the DUP is not required to commit to any aspect of power-sharing in advance of such certainty."
However, the two governments later said that it was his intention to accept the nomination after "all the conditions agreed at St Andrews have been met".
Taoiseach Bertie Ahern said Mr Paisley has now provided the clarity that was missing from his statement in the assembly.
Mr Ahern said the statement was welcome and had removed the doubt that had been raised about the DUP's approach to power-sharing.
A group of DUP assembly members also said their party had not taken part in any process to nominate a team to head up a future Stormont administration.
After the abandoned assembly meeting, 12 DUP assembly members signed a statement saying that they not had taken part in a designation process.
It said "nothing that we have said or done" could be taken by the government as such an indication.
The statement was signed by four of the party's nine MPs.
Nigel Dodds, the Rev William McCrea, Gregory Campbell and David Simpson all signed the statement.
It read: "Given the total lack of movement on behalf of Sinn Fein on the issue of support for the rule of law, the courts and the Police Service of Northern Ireland, nothing that we have said or done today can be taken by the Government as an indication that they can imply shadow, designate or any other status to anyone in relation to the Office of First and Deputy First Minister."
It was also signed by Lord Morrow and his fellow assembly members Diane Dodds, Paul Girvan, Stephen Moutray, Nelson McCausland, Mervyn Storey, Tom Buchanan and assembly deputy speaker Jim Wells.