The Irish Red Cross says Ukrainian refugees should start moving into pledged accommodation shortly.
It comes as emergency accommodation in the Millstreet Arena in Co Cork opened its doors to 70 people on Wednesday night.
It is expected to be full by the end of the week.
Ministers have said other large scale accommodation centres will likely be set up.
Liam O'Dwyer, secretary-general of the Irish Red Cross, told The Pat Kenny Show the first batch of pledged accommodation is being filled.
"We have sent the first tranche of the properties that are available and useable over to the department.
"I think they have moved those out now to the local authorities, and to other implementing partners.
"So we're hoping to see an increase in the number of people moving into those accommodations".
He says they also made contact with thousands of people over the weekend.
"We certainly sent out an e-mail over the weekend, we sent out actually 17,000 e-mails, just to make certain that we had covered everybody who was not contactable or hadn't been contacted yet.
"We received over 50% of the information back - so we got 8,755 responses.
"The vast bulk of them - nearly 80% of those - were positive to say 'Yeah look we're still in'.
"Then 2,042 people came back to say 'Look we've changed our minds'... that's about 22%.
"When you look at the overall figures... non-contactable are 9,184, and then the withdrawals are running at about 16% - which is 3,807."
'Some took refugees in themselves'
He says there are several reasons why people might pull out.
"People's circumstances do change, [maybe] people haven't thought about six months having somebody in the house.
"Or people may not have talked to their family - or indeed some people actually have gone ahead and taken Ukrainian refugees in themselves".
And he says he believes local authority emergency accommodation, while well-intentioned, should not be used medium-term.
"I think the number of emergency places that have been created, and the fact that their is other emergency accommodation in terms of the institutional buildings becoming available... I think that'll all be a help.
"But there is a reality that some of the emergency accommodation put together by local authorities, who are genuinely trying to respond, is probably not the type of standard that we'd all aspire to.
"But to be fair, it is being done on an emergency basis".