The blaze, at Seagoe Orange Hall, was reported to the Fire Service at around 2.30am yesterday.
The attack happened hours after a meeting between the Parades Commission and the Garvaghy Road Residents Coalition (GRRC] on Wednesday night.
Orangeman David Jones told the News Letter yesterday that the culprits broke into the back of the Orange Hall sometime between 1am and 1.30am and attempted to set the oil tank alight.
Describing the attack as "premeditated", he said the damage caused to the recently renovated hall would cost thousands of pounds to repair.
Mr Jones said: "They tried to set the oil tank on fire then used petrol to set alight to the inside of the hall causing extensive damage to the inside, destroying the banner of the lodge, pictures, windows and chairs."
Mr Jones, a press officer for Portadown District LOL 1, said the 20 members of the historic Orange hall were extremely upset by what had happened.
"People feel very annoyed and disappointed because £12,000 has been spent on renovating the hall," he said.
"It's hard to understand the mindset of people who think they are going to gain something by doing this type of thing."
Mr Jones added: "The Orange Order will not be intimidated by anyone. We have just as much right to live in society as other people have. We are going to occupy the hall and won't be scared away from it."
Drew Nelson, Grand Secretary of the Grand Orange Lodge of Ireland, said there had been an "unacceptable" number of attacks on Orange halls in the past few years.
"This is the 275th Orange hall burnt during this campaign," Mr Nelson said.
"We are in a new political dispensation now and we seem to be the ones that are losing out the most. We have had 19 Orange halls burnt this year, which is the highest figure for about seven years now."
Fr Martin McAlinden, parish priest of Moyraverty in Craigavon, condemned the arson attack on the hall.
"Such an attack is reminiscent of a past which the vast majority of us are glad to have moved away from," he said.
"The destruction of a building that represents the culture of a particular group in this area is shameful and an attack on the Orange Order and the community of Seagoe."
Meanwhile, after meeting the Parades Commission on Wednesday night. The Garvaghy Road Residents Coalition said last night that any mediation with Orangemen must be "wider than one particular sectarian march".
A GRRC statement said the process must include "discussion of possible alternative routes and venues for such disputed parades and events".
A Parades Commission spokesman said it was working to create a situation where the two parties were comfortable enough with each other to sit down and discuss possible chairmen for the process.

Editor's note:
An earlier online edition suggested that there may have been a connection between a meeting of the Garvaghy Road Residents' Coalition and the Parades Commission and the arson attack. We would like to make it clear that there is no evidence that the GRRC was in any way involved in the incident.