It comes after a suspicious object found close to St Joseph's Primary School in Donagh was reported to police earlier on Wednesday.
A number of businesses have been forced to close but no homes have been evacuated.
The crossroads of Royal Oak Road and Lettergreen Road in the village have been closed.
At Ballagh Crossroads the Dernawilt Road is closed and traffic is being diverted along the Ballagh Road and Cloghegaddy Road
The Kilnabrock Road Crossroads is also closed and diversions are in place along the Carneyhome Road and Mulnahonn Road.
Sinn Féin Fermanagh & South Tyrone MLA Sean Lynch has criticised the PSNI's handling of the alert.
"Local people's lives are being put at risk both by those that left this device and by the inaction of the PSNI," he said.
"I understand the PSNI's need to be cautious when approaching such reports but to allow people just to travel past the suspect device is irresponsible. The PSNI have a duty to protect the public and their failure in this incident to observe that does not instil confidence in the local population."
DUP MLA for Fermanagh and South Tyrone, Arlene Foster said those behind the series of recent security alerts do not have support from the community.
"They are unrepresentative and only serving to inconvenience hardworking people who want to get on with their lives," she said.
"Such actions are not furthering any political objective or ideal. They are the deeds of cowardly terrorists who operate under the cover of darkness and in the shadows."