The parades working group has a fortnight to complete the work
Six assembly members - three from the DUP and three from Sinn Fein - have held the first meeting of a working group set up to discuss parading.
Jeffrey Donaldson, Stephen Moutray and Nelson McCausland from the DUP met Gerry Kelly, Michelle Gildernew and John O'Dowd from Sinn Fein.
The group will meet every day until 23 February to arrive at a solution which can achieve cross-community support.
Mr Kelly said the atmosphere at the first meeting was "business-like".
"We have not said that we will sort out the issue of contentious parades in two or three weeks - we will try to put together a structure that will make it easier," he said.
But SDLP justice spokesman Alban Maginness said his party should have been included.
"We have talked constantly about democratic inclusion. That is the ethos of the Good Friday Agreement. If that is what the first and deputy first ministers are committed to, then it is a very strange omission," he said.
Sinn Fein's John O'Dowd insisted no-one was being excluded from the process.
"It would be perfectly natural for Sinn Fein and the DUP to prepare a report for the Office of the First and Deputy First Minister to be handed over to the Assembly," he said.
"The Assembly committee dealing with this is chaired by the Ulster Unionist Party and made up of all the parties - the Assembly itself has to vote on this on a cross-community basis."
The DUP's Nelson McCausland said it was important to take "a positive and constructive approach" to the process.
"I believe the Parades Commission has been part of the problem rather than the solution and what we are looking for is a new start," he said.
"We want a new system that will involve a greater emphasis on local accommodation, a better framework for mediation and a more acceptable system of adjudication - lot of the adjudications up to now were incoherent and inconsistent."
Orange Order historian Clifford Smyth said much of the groundwork had already been done in the review of parading chaired by Lord Ashdown.
"It's possible that they're building on other men's foundations, so this short deadline can be set because they're merely tweaking what's already known to be in the background," he said.
The first and deputy first ministers have agreed to support the outcomes of the parading discussions.
The Hillsborough Agreement said it recognised the need for "local people providing local solutions".
It also said that any framework should reflect "respect for the rights of those who parade, and respect for the rights of those who live in areas through which they seek to parade".
Following the completion of the consultation process a bill will be finalised.
The first and deputy first ministers have said they will support all necessary steps in the Assembly to ensure that the Bill completes all stages before the end of 2010.