Leaders from all five main assembly parties in Belfast are currently involved in efforts to decide who will be the North’s first justice minister.
David Ford of the moderate unionist Alliance party is likely to be the default candidate but he has so far refused to accept the position.
He published proposals for a programme for government for policing and justice but said he would not allow himself to be put forward until his party’s demands were met.
“We need to see progress on building a shared future for the people of Northern Ireland and we need to see a group conversation for the department of justice which would ensure that it delivers for all of the people of Northern Iretend,” he said.
He said there had been some “frostiness” at the justice meeting but added that Sinn Fein and the DUP were prepared to engage.
The SDLP nominated its North Belfast assembly member, Alban Maginness, for the position, which it said should be allocated under the existing d’Hondt rules for sharing out of ministries in the Six-County Executive.
New party leader Margaret Ritchie said that although her party welcomed progress made on devolution of policing and justice powers from London to Belfast at the Hillsborough talks last week, the agreed process to appoint a new minister was “a corruption of democracy”.
“There should not be any departure from the democratic principles as enshrined in the Good Friday Agreement,” she said.
She said she had agreed to participate in more bilateral meetings with Mr Robinson and Mr McGuinness.
Sinn Fein president Gerry Adams accused Ms Ritchie of “setting narrow party-political interests above the needs of the peace process”. He pointed out that in any recreation of the Ministerial Executive, the DUP, as largest party, would be able to fill the post.
“The SDLP are now saying that they want d’Hondt to run,” Mr Adams said. “The fact is that if this were done the SDLP would hand the justice ministry to the DUP.”
Senior Ulster Unionist members members have met to discuss the Hillsborough deal. The party is expected to continue to scrutinise the agreement over the coming days.
“This in an ongoing process. The UUP believes that the devolution or policing and justice is too important to get wrong,” a spokesman for the party said.
Meanwhile, the 32 County Sovereignty Movement said the conflict in Ireland would not be resolved by “creating sub committees and working groups in Stormont”.
“No amount of British money can buy Irish acceptance of its presence in our country. Re-branding the produce of partition will not disguise partition for what it is; an affront to Irish sovereignty.
“The regime at Stormont will return to form just as British backed unionism always intended for it to be. Token nationalist involvement merely offers it a veneer of acceptability.”
Republican Sinn Fein also issued a statement calling on “all republicans opposed to continued British rule, be it from Westminster or Stormont, to join us in the continuing struggle for Irish unity and self-determination”.
Party Vice-President Geraldine Taylor said that the agreement at Hillsborough is “just a further indication of the depths that Unionised Provisionals will go to uphold British rule in our country”.
“They have now added the administration of British policing and justice to their already full ‘portfolio’ in administering British rule on Irish people in the Occupied Six Counties.
“We as Republicans know only too well the jackboot tactics they will employ against those who oppose British occupation and what we will have to endure in the future - history has show us what to expect.”