Arlene Foster and Martin McGuinness called for any Twelfth of July events to be done in a peaceful way - which would not undermine law and order.
Thousands of Orange Order members will take part in annual parades across Northern Ireland later today.
And, in a joint statement First Minister Foster, Deputy First Minister McGuinness and Justice Minister Claire Sugden appealed for a "peaceful, respectful and safe parading season".
They said: "As we move into a period which has in the past resulted in heightened tensions, we encourage everyone to conduct themselves in a dignified and lawful way.
"We all have a responsibility to show leadership and to continue to seek resolutions to contentious issues through discussion and ensure any difficulties are identified and resolved peacefully, thus showing respect for the views and wishes of everyone in the community."
Some 18 demonstrations are being staged to mark the 325th anniversary of King William III's victory over James II at the Battle of the Boyne in 1690.
The biggest demonstration will be in Belfast with two "flagship" events in Kilkeel, Co Down and Portadown, Co Armagh.
The Independent Loyal Orange Institution will also hold a separate parade in Portglenone, Co Antrim.
Last night, huge bonfires were lit on the "Eleventh night" to usher in the Twelfth commemorations.
While the vast majority of the 600 parades are free of trouble each year, the threat of disorder at a small number of marching flashpoints always has the potential to mar the day.
Thousands of extra Police Service of Northern Ireland (PSNI) officers will be on duty throughout the region and there are contingency plans in place to call on additional Mutual Aid support from other UK forces if required.
Undoubtedly the largest and costliest security operation will be rolled out in Ardoyne - a volatile community interface in north Belfast where attempts to end the bitter dispute over a contentious parade have failed.
The Parades Commission - a government-appointed body set up to rule on controversial marches - gave permission for the morning feeder parade to go ahead shortly after 8am with certain restrictions, but has prohibited Orangemen from three lodges passing along the road when they return from traditional celebrations elsewhere.
Instead, marchers and bandsmen will be stopped at police lines in the unionist Woodvale area close to where loyalists have manned a protest camp at Twaddel Avenue for the past three years.
The Crumlin Ardoyne Residents Association (CARA) has been granted permission for a counter protest comprising of 60 people.
There will also also be a separate picket from the hardline Greater Ardoyne Residents' Collective (GARC) which was widely blamed for orchestrating disorder during previous years and has vowed on social media to "mobilise hundreds" again.
Last year, spontaneous rioting broke out when loyalists clashed with police who had blocked access to the contested stretch of the Crumlin Road.
Empty bottles, bricks and stones were thrown at riot squad officers and at one point intoxicated youths broke through police lines and were dancing on the bonnets of the PSNI's armoured Land Rovers.
A teenage girl was also knocked down close to where crowds of nationalists had gathered at a row of shops on the edge of Ardoyne.
Some 24 police officers were injured, including one senior policeman whose ear was almost severed by a piece of flying masonry and another who required 12 stitches after his finger was bitten.
In previous years, republicans have rioted when Orangemen were given the go-ahead by the Parades Commission.
PSNI Chief Constable George Hamilton said he had been "encouraged" by the level of positive dialogue ahead of this year's Twelfth.
He told a meeting of the NI Policing Board oversight body: "I think it does a create a more optimistic outlook for the rest of the parading season."
Northern Ireland Secretary Theresa Villiers has also expressed optimism about the outcome of the day.
Meanwhile, in his pre-Twelfth message, Orange Order Grand Master Edward Stevenson said the Institution hoped to attract record numbers of tourists.
He said: "The Twelfth of July offers a unique opportunity for the Orange Institution and the bands' community to showcase our culture and heritage, and we are confident of welcoming increasing numbers of visitors, tourists and families to all of our demonstrations across Northern Ireland."