Minister of State for Integration Joe O'Brien has appealed for help from private entities, State entities and other State bodies to provide accommodation to International Protection Applicants over the coming weeks.
A spokesperson for the Department of Children said that between four and six good sized buildings are needed to house people in the immediate term.
Last week, 81 asylum seekers who arrived in Ireland were told there was no accommodation available to them when they sought international protection.
Eight more newly arrived adults were not offered accommodation when they presented over the weekend, bringing to at least 34 the number currently without State provided accommodation.
Around 55 people who had been turned away between Tuesday and Thursday last week were offered places at the Citywest Transit Hub from Saturday.
Last Tuesday, the State ceased offering accommodation to new arrivals without children, which the Irish Human Rights and Equality Commission has said is in clear breach of the State's human rights obligations to International Protection Applicants.
The Taoiseach has said the Citywest hub is not adequate alone and more reception centres are needed, adding that the Government is "trying to identify sites and places for that".
"We don't want people to stay living in hotels, B&Bs or Direct Provision when they could potentially move on and get employment and rent," Leo Varadkar told Newstalk.
"But at the same time, we don't want to be so harsh that we push people into homelessness and don't have a roof over their heads."
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Following a protest in Co Waterford at the weekend and an attack on a migrant camp in Dublin, Minister Joe O'Brien has requested help from other State entities.
He said there is too much reliance on private providers and more State owned or controlled accommodation is needed.
The protest in Waterford took place ahead of the scheduled arrival in the coming days of 69 people who are seeking international protection here, with more expected in the coming months.
Minister O'Brien said he is hopeful that the people of Lismore will realise that refugees and asylum seekers will add to the town.
"We are working on a model to engage better. I will be doing some work on that where we can engage in a more fulsome manner," he told RTÉ's Today with Claire Byrne.
"I understand and accept that information doesn't come as fully and as promptly as is ideal and I'm working to improve that process."
Also commenting on the Lismore protest, Sinn Féin TD for Waterford David Cullinane said the vast majority of people will welcome and support those that come to Ireland.
However, he said the core issue was poor information flow, and he stressed the importance of an effective communication strategy.
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Labour Party Councillor John Pratt said he first heard about plans for the Direct Provision centre in Lismore last Tuesday.
Speaking on RTÉ's Morning Ireland, he said a meeting was held with the superintendent and two other local councillors but no details about the plans were given ahead of that meeting.
Mr Pratt said this is not about asylum seekers coming to the town, but it is about the hotel that is to be used.
"It is the centre of the town. It's probably a 10% increase in the population of Lismore in one fell swoop, where GP services and other services are already under pressure, even the locals are finding it hard to get GP appointments at this stage," he said.
"So, I suppose I think it's more about the location and the consultation. Transparency has been absolutely appalling, even to this day."
Mr Pratt said locals were hoping that the hotel would open again, but for tourists.
He said he did not attend the protest yesterday, which he said was peaceful.
Reporting by Ailbhe Conneely, Laura Fletcher