Parading has emerged as the first hurdle facing the new devolution-saving pact between Sinn Fein and the DUP.
A working group to be set up on Monday has just two weeks to come up with firm proposals for a way forward on the controversial subject.
Failure to find a workable consensus could unravel the next stages of the deal, particularly the scheduled Assembly vote in early March on devolving policing and justice powers.
The loyal orders gave the deal a cautious welcome but said they intended to “examine in detail the aspects of the political agreement involving public assemblies and parades”.
It recently emerged that the DUP and UUP held secret talks with the Orange Order at its headquarters in December.
A spokesman for the Grand Orange Lodge of Ireland and the Royal Black Institution said it viewed the agreement as a “positive step forward”.
“Our initial reaction is that it is a positive step forward and we are pleased that people have been focusing on the issue of parading,” he said.
“Everyone must now work to find the best regulatory system surrounding public assemblies and parades and we remain committed to playing a continuing and constructive part in that.”
A spokesman for the Apprentice Boys was more upbeat, describing the agreement as “the new improved proposals on parading”.
“The prize of an agreed regulatory and adjudication system is one which all sections of the Northern Ireland community should welcome,” he said.
“We are heartened that our experience in Londonderry was of some assistance to those who worked for this outcome and trust that parading will now be seen as a cultural rather than a public order issue.
“As ever, our approach will be constructive and supportive.
“The Apprentice Boys of Derry look forward to what promises to be a new beginning to parading in Northern Ireland.”
Meanwhile, republican Breandan McConnaith of the Garvaghy Road Residents Coalition (GRRC) in Portadown said he felt it was “impossible to say whether or not that legislation meets proper human rights standards”.
He said that “the acid test for the proposals in relation to contentious parades will be how the right to live free from sectarian harassment is to be enshrined in law and how any proposals are placed within a framework based upon the European Convention of Human Rights (ECHR) in its entirety”.
“For the past 12 years, the GRRC has consistently taken the approach that the right to live free from sectarian harassment must be a central plank in any decision-making process relating to contentious marches,” he said.
“We have equally been consistent in stating the proper and full application of the ECHR in its entirety and not any selective or piecemeal application of the same, has a major bearing on the marching issue.
“We have made both those positions clear on many occasions to both the British and Irish governments, to various political parties, to the Parades Commission and to both the Quigley and Ashdown reviews of parades” he added.