The fire, which is being treated as deliberate, was first reported at about 11:00 BST on Sunday.
Eight fire appliances and 45 fire fighters are at the scene, including crew members from the Irish Fire Service.
The blaze has spread across a 5 kilometre area, crossing the border.
It is the latest of 435 reported wildfires since the beginning of May.
Group Commander Brian Stanfield said: "We believe this fire has been started deliberately and we believe there are still people in the area qho are starting fires.
"We'd like to appeal to members of the public. This is reckless behaviour, this is not just endangering the countryside, but it is putting people's lives and property at risk."

Restrictions are in place between 11:00 and 18:00 on two sections of Fishergate and were introduced on a trial basis on 31 October 2016 to reduce congestion.
Misuse of the lane has seen over 23,000 drivers receive £60 penalty notices.
A Lancashire County Council spokesman said almost 16,000 had already paid their fines and the restrictions would continue until a review in April.
Roger Lawson, from the Association of British Drivers, said bus lanes were "discriminatory" and without any actual benefits.
Councillor John Fillis said the changes, which are in place from Mount Street to Corporation Street and at the Butler Street junction, had had a "big effect" in reducing traffic levels over the festive period.
He said there was a "growing consensus that the measures worked" and as a result, he had "decided that the bus lane should stay at least until we are able to assess how the changes work at different times of year".
"We definitely don't want to issue any £60 penalty charge notices, but it is an important way for us to enforce these changes," he added.
"The aim is to help to reduce traffic build-up that has affected parts of the city centre at the busiest times."
Mr Lawson said bus lanes "don't encourage people to get on the bus".
"These arguments [about reducing congestion] are specious and used to attack the use of private vehicles," he added.

The firm successfully completed operational trials of the Train 2 unit ahead of it receiving shale gas ethane from the US this autumn.
New docks and a new pipeline network have been built to receive the gas.
The company said the move means it is now in "great shape" to run the plant at full capacity.
The KG ethylene cracker was unable to operate at full capacity in 2008, leaving Ineos "no option" but to close the second manufacturing unit.
Ineos said the US ethane will be used as a supplementary feed for the KG ethylene plant and will allow the plant to run at increased rates.
Gordon Milne, Ineos Grangemouth operations director, said: "With the successful completion of the Train 2 trial we are now in great shape to receive shale gas from the US and to finally run the Grangemouth plant at full rates.
"All the parts of the jigsaw are finally coming together and Grangemouth will soon be back in the premier league of European petrochemical plants."
The plant's chief executive John McNally said: "Bringing the site back into profitability is the best way to secure our future here in Scotland.
"We know that ethane from US shale gas has transformed US manufacturing and we are now a step closer to seeing this advantage being brought to here to Grangemouth."

The pedestrian, from Tyne and Wear, was struck by a Vauxhall Corsa on Crossing Boulevard in Dartford at 18:07 GMT.
The vehicle was located in Bexleyheath and a 22-year-old man and a 20-year-old woman from Dartford were arrested.
They are being held on suspicion of causing death by dangerous driving, failing to stop at the scene of a crash and perverting the course of justice.
The victim died at the scene. His next of kin have been informed.
Officers from the Serious Collision Investigation Unit have appealed for witnesses.
PC Jamie Woodhams said: "I would like anyone who saw the vehicle and has not yet spoken to police to come forward.
"The vehicle suffered windscreen and headlight damage and was driven away from the scene towards the M25."
The Northern Ireland Fire and Rescue Service (NIFRS) is attending a gorse fire in Alderwood Road near Clogher and Fivemiletown in County Tyrone.
[NEXT_CONCEPT]
More than £1.3m in fines were issued in the two months after a new bus lane was introduced in Preston city centre.
[NEXT_CONCEPT]
A second manufacturing unit at the Ineos KG ethylene plant in Grangemouth will be brought back to life eight years after it was mothballed.
[NEXT_CONCEPT]
A man in his 20s has died after being hit by a car while crossing a road in Kent on Christmas Eve.