The 42 refugees were due to leave their accommodation yesterday.
The Department of Integration says efforts will be made to keep Ukrainian refugees close to their accommodation in Offaly.
41 Beneficiaries of Temporary Protection were due to leave Elm Grove House in Birr yesterday, after the contract for the accommodation expired.
Eight of those are children, and a further eight are people living with disabilities.
19 of refugees have been offered alternative housing in the former convent in Banagher, but, as of Tuesday, the remaining 22 were uncertain about their future options.
The State says all accommodation provided by the Department is temporary in nature, and moves occur frequently.
Green Party Local Election Candidate in Birr, Ekaterina Koneva, says she's discussed the concerns with Integration Minister Roderic O'Gorman:
“We, community activists, community members, department officals and politicians should not have constant battles, we should work together to establish a strong and effective working system, where people's needs are prioritised before finances, and where the Government work quickly when facing challenges.”
Read more: Ukrainian Children "Devastated" At Being Told To Leave Accommodation