The Orange Order will accept the banning or rerouting of marches if the Parades Commission is replaced by a body it approves of.
Speaking after a meeting with Secretary of State Theresa Villiers its grand chaplain the Rev Mervyn Gibson said he hoped the talks chaired by Richard Haass could produce such a replacement body.
He said: "We are not looking for a body that will just let us walk where we want whenever we want but we want a body that is fair and transparent. We would absolutely accept its determinations, even if it stopped or put conditions on some of our parades."
Asked if the Order would accept rulings it believed to be wrong, the Rev Gibson said: "Exactly, that is democracy. If we think they are wrong we will still accept them."
The Rev Gibson was part of a high-ranking Orange delegation which met Ms Villiers yesterday. Other members included grand master Edward Stevenson and Drew Nelson, the grand secretary.
He said the delegation had assured Ms Villiers that: "The Haass talks came up as an opportunity that the Orange Order, along with others, are going to grasp.
"We looked forward to a fair and equitable and transparent body to deal with parades emerging from this process."
The Parades Commission is the legal body set up to encourage dialogue between parading groups and residents or others along the route. It also adjudicates where dialogue does not take place or fails to resolve differences.
It is appointed by the NIO. The Order has refused to meet it.
Ms Villiers said that she will devolve power over parading to the Stormont Executive if local parties can reach agreement on how to proceed. Agreement seemed close at the end of 2010, when Sinn Fein and the DUP agreed a draft, but it was rejected by the Orange Order.
Mr Gibson said Ms Villiers told the delegation that Parades Commission determinations should be obeyed unless and until a replacement body was agreed. He said the delegation had listened to these comments without committing itself one way of the other.
The Order's position has softened somewhat since the Parades Commission was set up in 1998. At that stage the Order insisted on its right to "walk the Queen's highway" as an absolute civil right. It rejected bans on parades as undemocratic and also rejected discussions with nationalist residents.
Now the Order is open to dialogue in north Belfast, and had a limited engagement with residents there. Agreeing that some marches may legitimately be stopped or have conditions placed upon them is a new development.
"We have never bought into the Parades Commission because of the way it was enacted, because of their horrendous mistakes right from the beginning and because of their arrogance now. So we have never bought into the system. If we buy into the new system then we will have to accept their determinations and we will accept them," the Rev Gibson said.
The Police Federation has proposed a ban on contentious parades for six months and the SDLP has proposed a four-month voluntary moratorium. The Rev Gibson rejected moratorium calls.
"There is nobody looking for a moratorium only the SDLP and the Police Federation. Even Gerry Kelly of Sinn Fein seemed quite neutral on the idea," he said.
He branded the idea "undemocratic" and said it had not come up at the meeting with Ms Villiers.
Richard Haass, a senior former US diplomat and former American special envoy to Northern Ireland, will chair talks here in the autumn. They will deal with parading, flags and emblems and the legacy of our troubled past. The talks start next month and Mr Haass and his team must produce a report by the new year. The Police Federation has suggested that there be a moratorium on contentious parades for six months to facilitate its work.