Taoiseach Micheál Martin said Ireland has to move fast in terms of going through all the pledges, not all of them have been processed or gone through and there's some opportunities there.
Asked about people living in large communal halls, he said the number of public pledges of help “is not as large as originally anticipated”
It comes as the government is examining ways to financially reward people who give up their homes to Ukrainian refugees.
As the Irish Examiner reports, the move could be considered in the context of boosting the availability of refugee accommodation for fleeing Ukrainians.
Speaking on Sunday, Mr Martin said: “I think that's something that we're not ruling out, but that's something we can examine. Initially, it was never to be a monetary situation but you know, given in terms of the sustainability of that model, that's something that would always be under review.”
In terms of the influx of Ukrainian people fleeing the war, he said it is going to become extremely challenging because over 20,000 people have come into the country in a matter of weeks.
He said such an influx is unprecedented in terms of anything we have experienced before in relation to refugees fleeing a conflict zone and a war.
Children’s Minister Roderic O’Gorman said the State’s system to house Ukrainian refugees is “under pressure”, adding that the Government has “probably reached the limit” of the amount of hotel and guesthouse accommodation it can provide.
About 21,000 refugees have arrived into the country from Ukraine following the Russian invasion.
Of those, about 13,000 are being accommodated in State-provided accommodation, he told Newstalk’s On the Record:
We have secured over 3,000 rooms now at this stage and that’s the primary means by which we are accommodating people.
"We’ve also secured the use of maybe larger institutions, former convents and the like, and we’ll be looking to secure more of those going forward.
“Of course, a number will be accommodated in pledged accommodation as well, and that number is going to grow in the coming weeks.”
Mr O’Gorman said they have not needed to use military-style accommodation at Green Glens Arena at Millstreet, Co Cork, or Gormanston Camp in Co Meath “yet”.
“We’ve probably reached the limit in terms of the amount of hotel or B&B accommodation that we can provide, so it’s now looking at other sources, looking at those institutional buildings."