The Taoiseach has defended the Government's response as Ukrainian refugees were turned away from the Citywest hub in Dublin.
Thirty-three Ukrainian refugees who arrived in Ireland this week were told there was no accommodation for them yesterday.
All of them were first processed and given temporary protection status at Citywest.
The Department for Children, Equality, Disability, Integration and Youth has said that all of those turned away without accommodation were single men.
It said that no newly arrived women and children have been turned away.
The Capuchin Day Centre catered for more than a dozen Ukrainian refugees this morning, all carrying luggage.
RTÉ News spoke to a number of them who said they had spent last night sleeping in Dublin Airport after they were turned away from Citywest.
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Taoiseach Michéal Martin has defended the Government's response saying the State had not been slow and had instead been remarkably fast at responding to a wartime situation.
He said Ireland had responded in an extraordinary way in terms of the numbers it had already accommodated.
Asked why there was now a crisis when the numbers were anticipated months ago, Mr Martin said he did not accept that and he said nobody had predicted the scale of those arriving.
"The figures were not supposed to be higher, certainly not before the summer," he said.
"We can all estimate the numbers coming in but that doesn’t mean you can immediately provide accommodation.
"We will have to move faster to accommodate increasing numbers. There’s an intensification of the war and it’s taking a very nasty turn and civilians are now a target."
On 22 March, Minister for Agriculture Charlie McConalogue told RTÉ's Morning Ireland that up to 200,000 Ukrainian refugees could arrive in Ireland. On the same day, Tánaiste Leo Varadkar told the Dáil that 40,000 Ukrainians could arrive by the end of April.
A statement from the Department of Children, Equality, Disability, Integration and Youth on Thursday said over 58,000 people (42,000 Ukrainian, 16,000 international protection) had arrived in Ireland this year.
Mr Martin said a range of measures would come from different departments at a meeting on Monday including an increased incentive for host families.
Asked what people being turned away from Citywest are being told, he said they are simply being told that accommodation is not there.
Mr Martin was speaking at the Fianna Fáil president's dinner this evening in Dublin.
On Thursday, the department said that the Citywest transit hub was at capacity.
Minister Roderic O'Gorman said that while accommodation would be provided to the most vulnerable this weekend, others would not be offered anything and he could not rule out that people may sleep rough as a result.
International protection applicants are similarly being turned away without accommodation, but figures for how many have already been told there is no accommodation for them are not available.
Martin Heydon, Minister of State at the Department of Agriculture, Food & Marine, said the Government "cannot guarantee" a bed for every refugee arriving in Ireland.
Mr Heydon said the Irish Government and society has made huge efforts to deal with the scale of the crisis and the arrival of Ukrainian refugees.
'We are talking about 60,000 people who have come to our shores this year, who are seeking and who have been accommodated by the State. Today, that compares to 7,250 this time last year, that's the equivalent of the population of Waterford city," he said.
The Head of Policy and Communication with the Simon Community said the situation with Ukrainian refugees is very worrying and likely to get worse if large numbers continue to arrive.
Speak on RTÉ's Saturday with Katie Hannon, Wayne Stanley said that frontline services, such as Simon, will continue to try to support people, but there is not capacity in the system to house people.
This is a perfect storm, he said, and the next number of weeks are going to be very difficult.
Mr Stanley said he had experienced one or two isolated incidents of refugees rough sleeping, but outreach teams have not seen large numbers on the streets so far.
He said that vulnerable people are being triaged on arrival but warned that even families could get caught up in the crisis.
Speaking on the same programme, Mr Heydon said he understood that 33 Ukrainian men were processed at Citywest but were unable to be accommodated last night.
"We can't guarantee everyone who comes here a bed right now," he added.
He said this was "a really disappointing place for us to be in".
He said land that is earmarked for Housing for All should be used for modular housing for refugees and Irish people.
The Fine Gael TD for Kildare South said the Office of Public Works and the Department for Integration are undertaking a review of land in Kildare that has been identified for modular homes.
Marian Harkin, Independent TD for Sligo–Leitrim, said there is a delicate balance to be struck.
She said there is a duty to give shelter and safety but the country is at capacity.
Paul Murphy, People Before Profit TD for Dublin South-West, called for the Government to take more hotel rooms to house refugees and those facing eviction.
Mr Murphy said the State currently has 16,000 out of 62,000 hotel rooms.
He said vacant properties must be dealt with in the longer term.
Additional reporting Sandra Hurley