Mr Murphy met unionist politicians
The Northern Ireland secretary has appealed for calm during the Orange Order parades on the Twelfth of July.
Paul Murphy was speaking after separate meetings with the Democratic Unionist Party and the Ulster Unionists to discuss a contentious Orange Order parade in north Belfast.
The main focus of Sunday's talks was the restrictions placed on the return leg of a parade in the Ardoyne area on Monday.
Orangemen can walk past the nationalist Ardoyne area on their way home but the Northern Ireland Parades Commission has said they cannot be accompanied by bandsmen.
In response to the ruling, the Orange Order plans to hold a series of protests in several parts of the city at the end of Monday's celebrations.
It is understood that includes loyal order members blocking a number of main roads in and out of Belfast.
For the fifth day in a row on Sunday, women blocked the Ligoniel Road in protest at the commission's ruling.
Women protested on the Ligoniel Road on Sunday
Mr Murphy said: "I know how much hard work has gone into ensuring a quiet and peaceful summer.
"I would urge all political and community representatives to redouble their efforts in the coming days of heightened tension.
"I understand the frustrations of many involved but it is in the interests of everyone in Northern Ireland to be able to enjoy a peaceful and dignified Twelfth of July."
Assistant Chief Constable Duncan McCausland also appealed for a peaceful, dignified and lawful day.
Mr McCausland said: "People have a right to march as long as they do it peacefully and within the law. They also have a right to protest, peacefully and within the law.
"No one wants to see a situation where a parade or protest descends into violence and disorder."
Earlier, North Belfast MP Nigel Dodds and DUP colleague Nelson McCausland said the Parades Commission had made a "complete mess" of the parades' issue in north and west Belfast.
They said they had urged Mr Murphy to intervene to ensure that all those with authority realise the "seriousness of the current situation."
Orangemen have been angered by Parades Commission ruling
Mr Dodds said: "The Parades Commission has undermined weeks and months of good work on the ground.
"Illogical and bizarre decisions which have been taken by this unaccountable quango have done real damage."
Sinn Féin assembly member Gerry Kelly accused the Orange Order and unionist politicians "of deliberately heightening tensions" over the parades issue.
He said party colleague Martin McGuinness had spoken by telephone to Mr Murphy on Sunday.
Mr Kelly said: "The decision taken by the Parades Commission to force this parade through nationalist north Belfast twice on the Twelfth was the wrong decision.
"It is completely unacceptable that the nationalist community is being held
to ransom and threatened in this fashion."
Earlier, Ulster Unionist assembly member Sir Reg Empey called on Mr Murphy to overturn the Parades Commission ruling.
He said: "Because of the nature of some of these decisions it provokes people
and creates tensions and we are about avoiding those so that
we can have a peaceful Monday."
In a statement, the Parades Commission said it believed the law would be upheld by all law-abiding parties and participants.
The annual Twelfth demonstrations mark the climax of the Protestant marching season.
They mark the victory of William of Orange over Catholic King James 11 at the Battle of the Boyne in 1690.
The Parades Commission was set up in 1997 to make decisions on whether controversial parades should be restricted.