The DUP says it will consult the entire unionist community if and when, in its opinion, the IRA has moved from violence to democracy.
DUP deputy leader Peter Robinson led the delegation
DUP deputy leader Peter Robinson made the comments in an address to the British-Irish Inter-Parliamentary Body, in Killarney, County Kerry.
Mr Robinson said they were ready to begin this consultation once a "prima facie case" could be made over the IRA.
He said that no party had more to gain from a working assembly than the DUP.
During a wide-ranging speech, Mr Robinson said there could be "no acceptable level of paramilitarism or criminality".
"While it would be foolish to suggest that considerable progress has not been made, it would be dangerous to suggest or imply that this process has been completed," he said.
"I cannot say if or when a judgement can be made that completion has been reached, but if and when a prima facia case can be made, we have committed ourselves as a party, in our election manifesto, to a consultation process within our community."
He said unionists had to be satisfied the IRA's transformation was "stable and enduring and not tactical and strategic".
Mr Robinson said his party had "nothing to gain by unnecessarily delaying devolution".
"With over 30 MLAs, we are the largest political party in Northern Ireland and would have greater influence than any other party over decisions taken in the province," he said.
"It is in our interests, and more importantly, it is in the interests of the people we represent, that when the conditions are right we have devolution returned to Northern Ireland at the earliest opportunity."
Mr Robinson is one of four Democratic Unionist MPs who have travelled to the Irish Republic to address the body, which was set up to strengthen British and Irish parliamentary links.
However, the party denies the address means an end to its 16-year boycott of the body.
Martin McGuinness said the DUP must share power
The UUP continues to boycott the BIIB, which was established in 1990 to "contribute to mutual understanding".
The DUP was invited to Monday's session by the body's co-chairman, the former Northern Ireland Secretary Paul Murphy.
Irish Prime Minister Bertie Ahern said the attendance of the DUP was a "hugely important step".
He also said that there were "no circumstances" under which the British or Irish governments would go outside the 24 November deadline for the re-establishment of a power-sharing executive in Northern Ireland.
Sinn Fein's Martin McGuinness has said the DUP must be willing to share power with his party.
The Mid-Ulster MP was speaking after meeting NI Secretary Peter Hain to discuss the 15 May recall of the assembly.
Mr McGuinness welcomed the DUP's engagement with the British-Irish Interparliamentary Body and said it had "big decisions to make".
"But really the next stage in all of this is for the DUP to join with Sinn Fein in the formation of this power-sharing government and to take their places on the North-South Ministerial Council," he said.
"That is where this needs to go.
"I think the recent developments, while welcome, could be meaningless if all they are offering is a talking shop and they are not really interested in forming a government with Sinn Fein and the other parties."
The 68-member British-Irish Interparliamentary Body was established as a link between Westminster and the Dail (Irish Parliament).
It initially comprised 25 British and 25 Irish members drawn from the upper and lower houses of both parliaments.
In recent years the membership of the body has been extended with representatives from the Welsh Assembly, the Scottish Parliament, the Northern Ireland Assembly and the Isle of Man and Channel Islands.