Drew Nelson said members have organised protests that will be controlled by the Orange Order and will be peaceful.
At a joint news conference on Thursday, the order and unionist leaders unveiled the first part of their "graduated response" to a Belfast parade ruling.
Meanwhile, a court challenge to the ruling is due to be heard on Friday.
A judicial review hearing is expected to take place in the High Court in Belfast at 14:00 BST.
On Thursday evening, Northern Ireland Secretary Theresa Villiers said she would meet unionist and Orange Order leaders to discuss their call for a commission of inquiry into the issue of parades.
Speaking on the BBC programme The View, Mr Nelson said the institution was doing what it could could to ensure peace.
"We are stepping up to the mark here to try and manage this situation," Mr Nelson said.
"If we did nothing, it would create a more volatile situation and increase the risk of violence and we are doing everything in our power to stop that.
The Parades Commission, last week, ruled that the Ligoniel Orange Lodge should not make a return parade along a stretch of the Crumlin Road that separates unionist and nationalist communities on 12 July.
It is the second year in a row that such a ruling has been made.
Several nights of rioting took place after the same parade was stopped from returning along the road last year, with scores of officers injured.
The Orange Order's grand secretary has said the institution has put a massive effort into calming the situation in Northern Ireland ahead of 12 July.