In his weekly blog for the Belfast Media Group, the Sinn Fein president warned that society “cannot afford the negative and unsustainable political, financial and social costs from parading disputes”.
Both McDonald and Adams have said there should be no march on the Garvaghy Road in Portadown without the consent of local residents.
Their comments come as a Stormont working group gets ready to report on “a new and improved framework” to rule on parades.
“There are over three thousand Orange marches in the north every year,” Adams writes.
“Generally speaking they pass off without any great fuss, not least because of the tolerance of everybody else. There are a small number of contentious parades which for years caused considerable difficulties.
“One of the big problems incidentally touched on by a loyalist leader Jackie McDonald this week is that the Orange would march into an area where they were unwelcome and leave everybody else to deal with the consequences in the weeks and months afterwards.”
In an interview with this newspaper yesterday, UDA brigadier McDonald attacked “triumphalism” linked to marches, and also criticised Sinn Fein’s involvement with protests, saying that had “polluted” the atmosphere.
In his blog, Adams writes: “That the lid was generally kept on some of these areas is down to local residents and Sinn Fein representatives.
“But there has also been good steady work done by others on the unionist side, including sensible people in loyalist and community organisations.
“Irrespective of the differences between us there is clearly a need to focus on how to resolve the remaining handful of contentious parades in a spirit of mutual respect.”
In Portadown and on the lower Ormeau Road in Belfast, McDonald believes that should involve Orangemen walking away.
Adams says the challenge is “to go beyond settling contentious parades”. “We need to build a new relationship of tolerance and respect,” he writes.
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? email@example.com