The Tánaiste has said that up to 40,000 Ukrainians could arrive in Ireland by the end of April.
Leo Varadkar told the Dáil this would result in a 1% increase in the country's overall population, which will place pressure on many services.
More than 10,000 people have arrived in Ireland so far.
Speaking on his way into Cabinet this morning, Mr Varadkar said it was hard to say what the figure will be beyond that.
"It could easily be 30-, 40,000, maybe more than that, and in the context of our population that would be nearly a 1% increase in our population in a matter of a few weeks."
The Tánaiste outlined the impact it would have on education, housing and other services and described it is a rapidly changing situation.
He said the Government intends to provide every Ukrainian with "own-door self-catering accommodation" in the long-term, but said it will be a challenge and there is "no point pretending otherwise".
He said in the short term they will largely be housed in hotels and B&Bs.
Mr Varadkar also said possible further sanctions on Russia by the EU was set to be discussed at Cabinet today as he condemned Russia's actions in Mariupol as "war crimes".
The Taoiseach asked the Tánaiste to chair today's Cabinet meeting. Micheál Martin was still attending the meeting via video conference from Washington.
The memo going before ministers did not specify numbers of refugees, but senior Government figures are planning on the basis that 2% of the 10 million people expected to flee Ukraine could possibly come to Ireland.
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The Government was due to hear how this would place further pressure on accommodation and services.
A search for potential housing is continuing across Government departments and local authorities with planning laws expected to be set aside to find homes quickly.
Gardaí will soon be able to carry out vetting within seven days on perspective homes pledged by the public.
This will only be required in cases where a child or a vulnerable adult is being placed in shared accommodation.
The Cabinet was told today that the cost of accommodating 1,000 people in a hotel for a year is €33 million with some supports included.
However, this cost does not include social protection payments.
There are currently more than 4,300 people from Ukraine staying in hotels here.
The Government has block booked over 2,200 hotel rooms as part of the State's humanitarian response to the war in Ukraine.
Liam O'Dwyer, Secretary General of the Irish Red Cross, said that they have received 21,000 pledges of accomodation, "which is astonishing".
"Just under a thousand" were received during the Syrian crisis, he noted, speaking before the Joint Committee on Foreign Affairs and Defence, which was discussing the humanitarian crisis in Ukraine.
Minister for Foreign Affairs Simon Coveney said there would not be a limit on the numbers coming to Ireland from Ukraine, as he said this situation was not about "normal capacity ceilings".
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He said it would not be acceptable for Ireland to say it can only do so much, as he referred to a "collective responsibility as Europe responds to the enormous challenges of this war".
"This isn't a question of whether we can accommodate X amount of people, it is about how we will. This is a war effort," he said.
Mr Coveney added that it requires a "big national effort" and he expects an extraordinary outpouring of support from people in Ireland.
She said the latest figures show that 7,326 people arriving from Ukraine have been issued with PPS numbers.
She said 88% of those issued with PPS numbers are women and children.
"We're providing the people with the PPS numbers which means that they have access to many other services across the state, providing people with financial support that starts with supplementary welfare allowance and child benefit," she said.
She said they are also putting them in contact with support centres around the country.
The Minister for Integration and Equality Roderic O'Gorman has said his department is focused on assisting around 4,700 Ukrainians with accommodation.
Speaking at a press conference following the Cabinet meeting, Mr O'Gorman said that accommodation is primarily provided in hotels with 2,000 hotel rooms currently being used to accommodate Ukrainian refugees.
He also said Tusla is providing accommodation to 22 unaccompanied Ukrainian minors who have arrived here.
Regarding the medium-term plan, he said his department is working closely with other government departments regarding possible accommodation options.
"We're engaging with religious orders in terms of potential large religious properties or buildings that may be available, engaging with other State bodies and agencies in terms of properties that may be available there," he said.
He said it is "only 27 days into this crisis" and "there is significantly more work that needs to be done".
Minister O'Gorman said the Government is aware of the scale of the challenge to house so many refugees but gave the assurance that very significant work has been done in terms of sourcing available properties.
"We have acted very quickly to meet short term needs of individuals."
He said accommodation is being sourced across "all areas of society" and that this is the only way to respond as it allows a "degree of flexibility" if there is a surge in the numbers arriving here.
He said the Department of Housing is looking at all options, including student accommodation and also referred to the efforts by local authorities to identify properties, with 500 sourced so far.
Minister O'Gorman said the Government recognises the Ukraine crisis as a major challenge and he believes it will be a huge element of what this government focuses on for the rest of their term in office.
Additional reporting Mícheál Lehane
