It follows last Sunday morning’s raid on O’Kane’s Filling station on the Feeny Road just outside Dungiven.
A stolen digger was used by a gang to rip the machine of the wall of the building and dump it into a Citroen Berlingo car which had a hole cut out in its roof.
Police have increased patrols in rural areas across Co Derry but the gang or gangs continue to evade the PSNI dragnet.
Across the border in Co Donegal, Gardai are on high alert after the recent theft of two pieces of heavy plant machinery.
Faughan councillor Paul Fleming said: “Sunday’s incident is yet another attack on our rural communities which saw the ATM being stolen from the shop and filling station.
“Many shop owners are now living in constant dread that their premises may be next.
“I would urge the PSNI to increase resources to their dedicated task-force probing ATM thefts in order to tackle this latest spate of robberies across the North.
“There is a real concern among communities that these events will lead to the removal of vital ATM facilities from rural towns and villages, areas that have already had other services withdrawn.
“Such a move would have a detrimental effect on how people live and do business in rural areas.
“I would urge anyone with any information to bring it forward to the PSNI to help catch those responsible.”