Published Monday, 22 February 2010
Mr Dodds rounded on Mr McGuinness as the parades working group, made up of representatives from Sinn Fein and the DUP, met at Stormont to complete the task it was set in the Hillsborough agreement.
The six-strong group, which was asked to formulate new proposals to manage controversial loyal order marches, will present its finding to Mr McGuinness and DUP First Minister Peter Robinson on Tuesday.
'Orange state'
The latest spat came after Mr McGuinness's remarks at an event in Strabane, Co Tyrone to mark the deaths of three IRA men.
"The Orange Order has to sit up and take notice that the world is changing all around them, that the north is not an Orange state - recognise that not alone have the old days gone, but the days of the triumphalist Orange marches through areas where they are not wanted have to be consigned to the history books forever," he said.
He also criticised the Orange Order leadership for continuing to refuse to engage with republicans.
"And they should come forward, like men and women, and come into rooms, sit and talk to representatives of the nationalist/republican community in areas where they are seeking to march.
"Thus far, they have refused to do that, but that's what they must do in the course of the coming period."
Mr Dodds reacted angrily to the Sinn Fein MP's speech.
"At a time when people are strenuously working for a resolution to outstanding issues, Mr McGuinness decides to play to his own gallery with a cliche-ridden attack on the Orange Institution," he said.
"That sort of republican propaganda might play well with his hardcore supporters, but it will not instil community confidence throughout Northern Ireland on other important matters.
"Mr McGuinness needs to show some leadership and stop looking over his shoulder at the dissidents (republicans) and the SDLP. Sinn Fein should focus their efforts on getting a new start to parading.
"It is ironic that Martin McGuinness should have talked about the so-called human rights violations caused by celebrations of Unionist culture at an event dedicated to the commemoration of people who were human rights abusers. Terrorists denied thousands of Ulster people the ultimate human right - the right to life."
On Monday residents' groups from the Lower Ormeau road in Belfast and the Garvaghy Road in Portadown, Co Armagh published the submission they sent to the working group last week.
They said they were making the correspondence public because they were concerned that the group's final submission to the First Minister and deputy First Minister would not be disclosed.
"This would be counter to any sense of openness, transparency and fairness regarding this process," Gerard Rice from the Lower Ormeau group and Breanan Mac Cionnaith from the Garvaghy Road body wrote in a joint letter.
On Saturday, Orange Order leaders expressed concern over some of the potential measures being considered by the working group.
After a three-hour private meeting in Co Tyrone, Grand Master Robert Saulters said members were uneasy about some of the possible changes.
"Our membership have several issues of concern about the proposed arrangements that may come from the current parades working group and are in no position to make any judgment or form any opinion at this time," he said.
The Orange Order initially welcomed the Hillsborough Agreement's promise of a new system for overseeing marches fiercely opposed by nationalist residents' groups.