Sinn Fein deputy first minister Martin McGuinness has called for an "earnest endeavour" at the start of all-party talks about paramilitarism and welfare reform.
Creating a workable budget for the devolved institutions at Stormont and implementing last year's Stormont House Agreement will be part of discussions covering the next four weeks.
The largest parties attended the meeting in Belfast called by the British and Irish Governments.
Mr McGuinness said: "Our position is that the IRA are gone, that they represent no threat whatsoever.
"What we need to do is find a way forward that ensures a workable budget for the Executive, the implementation of the Stormont House Agreement and the British Government living up to its responsibilities and also to find a way forward which allows everybody to be involved in earnest endeavour."
He said there were people in parts of Belfast and Londonderry who "masquerade" as republicans and purported to be the IRA, adding to the mix of confusion about whether the IRA existed.
Mike Nesbitt, leader of the Ulster Unionists, said unblocking the impasse over welfare reform could include providing money for mental health; cash unspent on legacy issues covered by the Stormont House Agreement could be used for welfare.
He added some £20-£25 million of legacy money for historical investigations will be lost to the Northern Ireland Executive this financial year, due to the impasse in implementation of the Stormont House Agreement.
"London has already conceded the principle of funding legacy issues.
"There is no reason why the UK Government should not offer additional funds for Northern Ireland's mental health issues which are legacy and not covered by the Barnett Formula (which sets funding for devolved regions) and therefore unlike welfare have no implications for Scotland or Wales."
He acknowledged an "inconsistency" in his party attending the negotiations when it was not sitting in the Executive but added he would make his position clear to the other parties.
He added: "Even if we get through welfare there are huge and fundamental issues to be resolved and we will be uncompromising in terms of putting it to others to live up to their responsibilities as we will live up to ours."
Senior Democratic Unionist Arlene Foster said the talks would be intensive and her party was in solution-finding mode.
"We never for one moment thought there would not be a continuation of criminality and criminal activity because we know some people are wedded to criminality but we have to make sure that it does not seep into the democratic institutions of Northern Ireland."
She added: "We want the Stormont House Agreement to be implemented and want to be able to make sure that Stormont works for everybody in Northern Ireland."
David Ford, leader of the cross-community Alliance Party, said his team was in determined mood.
"I have got children in this society, I have got grandchildren in this society. I am fed up with the notion that we have quick fix, year after year.
"What we have to do is solve the problems and really engage."