The Orange Order has held parades for two centuries
Members of the Orange Order are concerned about new proposals on controversial parades drawn up by a DUP and Sinn Fein working group.
Speaking after a special meeting of the order on Saturday, Grand Master Robert Salters said reservations were voiced.
But he said they were in no position to make any judgement or form any opinion at this stage.
The DUP and Sinn Fein set up a six-strong group to review parading following the Hillsborough Agreement.
That working group is due to report to deliver its report to the office of the first and deputy first minister on Tuesday.
Initially, the Grand Orange Lodge of Ireland and the Royal Black Institution welcomed the agreement.
They described it as "a positive step forward" and said they were committed to playing "a continuing and constructive part".
About 100 members attended this weekend's meeting of the Grand Lodge of Ireland in Tamnamore near Dungannon which lasted two and a half hours.
It was an opportunity to discuss updates from DUP members on the parades working group.
Afterwards, Mr Saulters said there were "several areas of concern".
The remit of the six-strong DUP/Sinn Fein parades working group is to agree a framework for dealing with what is a particularly controversial issue in Northern Ireland.
Three Democratic Unionist and Sinn Fein members have been tasked with designing a new and improved framework to rule on controversial marches, including a focus on local solutions, mediation and adjudication.
Nationalist residents in mainly working-class areas like north Belfast and Portadown, County Armagh, oppose Orange Order processions in their areas because they view them as triumphalist.
Members of the loyal orders accuse residents of going out of their way to be offended and maintain it is their traditional right to demonstrate on the streets.
Speaking ahead of Saturday's Orange Lodge meeting, the grand secretary of the Orange Lodge, Drew Nelson, said members were determined that the Parades Commission should be abolished.