Those who targeted Mulnagore Orange Hall in Pomeroy "seem determined to drag us back into the past" says Mid Ulster Councillor Ken Reid.
Hitting out at recent vandalism and damage to the door, down spouts and lights at the premises, Cllr Reid said he was "greatly annoyed" by the incident, which saw 'republican slogans' daubed on the door.
Mullnagore Orange Hall is understood to have been targeted around January 10 this year.
Chief Inspector Mervyn Seffen said: "Graffiti has been scored onto the door of the building and damage caused to down spouts and security lights. The damage was reported to Police on January 10th. Enquiries are continuing, however, if anyone noticed suspicious behaviour in and around the area, they are asked to call Police on the 101 number."
"When I was informed of the attack on Mulnagore Orange Hall I was greatly annoyed and disappointed that the Orange Community is still been targeted by people who seem determined to raise tensions and drag us back to the past," Cllr Reid added.
"The Orange Order is of no threat to anyone and I can't understand why the person or persons who carried out this act of crime against an Orange Hall which has caused no harm to anyone, feels that they have the right to graffiti the hall with republican slogans and cause damage to the halls exterior fixings.
"This crime will not be tolerated and I would call on anyone with information to contact the PSNI as such attacks must end and the person or persons who committed this crime must be brought before the justice system. "
Kieith Buchanan, DUP MLA for the area, said: "I condemn the recent attack on Mulnagore Orange Hall in a moment of madness by desperate individuals, I have been speaking to several members and this type of attack offers nothing to society or any community.
"As a proud and active member of the institution this does nothing to further any cause by anyone and confirms the 'respect' terminology has certainly more than one understanding.
I now call upon the PSNI to do their job and apprehend those involved."
Mid Ulster UUP MLA, Sandra Overend, has also condemned the attack.
"I was appalled to hear that Mulnagore Orange Hall has been attacked, with graffiti written on the door, and a spouting and security light damaged," she said.
"This act of vandalism demonstrates a complete lack of tolerance and respect for property and for the Orange tradition in the Pomeroy area, and must be condemned.
"This is not the first attack on the Mulnagore Hall, but those responsible for this incident have nothing to offer society, and will not succeed in their attempts at intimidating the minority unionist community in this area.
"If anyone has any information regarding this incident, I would ask that you please contact the PSNI as soon as possible."