Senior figures in the institution made the call when the met with top police officers on Thursday, in a meeting which the order described as a “useful exercise”.
The meeting involved Orange Grand Master Edward Stevenson, Assistant Grand Master Lewis Singleton, and Assistance Chief Constable Stephen Martin, among others.
It comes against a backdrop of attacks on Orange halls ranging from graffiti and the removal of flags to the destruction of halls through arson.
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For example, Salterstown Orange hall in Co Londonderry was badly-damaged in an arson attack in the early hours of last Monday.
The order said that it was “the 21st reported incident targeting Orange property so far this year”.
After the meeting, which took place in the PSNI’s Knock headquarters in east Belfast, Mr Stevenson said: “While we have regular communication with the police, it was of paramount importance that we held this meeting to convey our deep concern at the upsurge of criminality targeting Orange halls.
“In our discussions, we underlined the seriousness of the situation and the seemingly unending campaign of violence against our properties and way of life.
“We highlighted the fact no part of the Province is exempt from such sectarianism, with halls in every county targeted.
“We were disappointed to be informed of the zero conviction rate, so far this year, for such hate crimes.
“Whilst mindful it is logistically impossible for a 24 hour guard on every hall, we emphasised the need for a concerted and co-ordinated policing strategy, resulting in individuals being made amenable for their criminal activities.
“Grand Lodge is willing to assist the PSNI in whatever way possible in this regard to ensure the prevention and cessation of such attacks.”
He also stressed that the responsibility for curbing attacks was not just down to the PSNI, but for wider society as a whole to “confront sectarian attitudes”.
Mr Stevenson has also raised the issue with members of the Policing Board; the panel which essentially monitors the work of the PSNI.
In a statement on Thursday night, Assistant Chief Constable Stephen Martin said: “I was pleased to have been able to meet with the Grand Master of the Orange Order and his senior colleagues today. This was a useful and productive meeting.
“The PSNI condemns attacks and criminal damage on all property irrespective of where it occurs or which community is the victim.
“We are aware of the concerns expressed by the Orange Order and want to assure them that we view these attacks seriously.
“Each incident is investigated and all available evidence is obtained with a view to making any identified offender accountable through the criminal justice system.
“We would encourage anyone to report incidents of this nature promptly and to assist us in our investigations if they have any information.
“Anyone who has information about who is behind any attack should contact police on the non-emergency number 101. Information can also be passed anonymously via the Crimestoppers charity on 0800 555 111.
“We will play our part but others have a part to play too.
“This is a time for everyone to show civic responsibility, to support their neighbours and to demonstrate to those few who would seek to disrupt the lives of the many that they will not succeed.
“We need evidence which can bring those responsible to court and secure a conviction.”