The asylum seekers were due to be moved to a facility in Offaly.
The Department of Integration says it will work to find suitable alternative accommodation in the Borrisokane area for families at an IPAS centre.
A protest has been organised for this evening against plans to move the asylum seekers out of the town and into a facility in Birr in Offaly.
The families at Riverside IPAS centre have completed their international protection applications and have access to the full range of housing supports available to Irish residents
The Department say when an alternative becomes available, it's important for Riverside to provide accommodation for those still in the application process.