There are now 512 recently arrived asylum seekers who have not been offered any State accommodation, according to the latest figures from the Department of Integration.
That is 55 more international protection applicants left without shelter since Friday and 136 more since this day last week.
All the asylum seekers who have not been offered accommodation when they presented seeking international protection are men.
The department stopped offering accommodation to all asylum seekers on 4 December amid a "nationwide shortage".
There have been a number of recent protests at properties that were intended to be used to house male asylum seekers and gardaí are investigating suspected arson at the Ross Lake House hotel in Rosscahill, Co Galway, in December, which was among them.
To date women and children seeking international protection have been accommodated, however yesterday, the department said that there is now also "an acute shortage of accommodation for families and children".
This is the second time in 12 months that the Government has ceased offering accommodation to all eligible asylum seekers when they present seeking international protection, due to a shortage of available places.
Last year between 24 January and 15 June, a total of 1,542 asylum seekers were not initially offered accommodation when they first presented.
However the numbers being left without shelter are climbing much more steeply this time around, reaching 500 in little over a month.
It took almost three months for the number of international protection applicants left without shelter to reach more that 500 last year, a number described by the UN Refugee Agency as a "grim milestone".
Since 4 December, 659 new male international protection applicants have presented to the International Protection Office.
Of those, 80 were accommodated following what the Department described as an "availability and vulnerability triage".
A further 67 who were initially not offered any accommodation were subsequently offered a space, with just one person offered a place since Friday.
Read more: Dept 'engaging' with Mayo hotel over plan to house asylum seekers
Irish Refugee Council 'gravely concerned'
The CEO of the Irish Refugee Council Nick Henderson has said he was "gravely concerned by the situation".
"People are not safe and very cold weather is forecast, there is no adequate plan in place to meet this crisis" he said, adding that it was "a breach of our obligations under Irish and EU law which cannot be wished away".
Mr Henderson said that the Irish Refugee Council has met more than 70 international protection applicants without accommodation.
"Some are sleeping rough and are moving around the city, people are desperate and cold and sometimes face hostility, one person reported having is tent stolen, one was assaulted.
"Some people report physical and mental health problems exacerbated by sleeping rough," he said.
Weekly payments for asylum seekers who are not offered accommodation have been increased by €75 to €113.50, and they are also provided with the details of homeless day services.
Aubrey McCarthy, who is the founder and chairman of Tiglin, which runs the Lighthouse Homeless Cafe on Pearse Street in Dublin said yesterday that it had seen a surge of demand for its service, and an increase in presentations by asylum seekers was contributing to that.
He told RTÉ's Morning Ireland that the service was focused on helping people who are facing "tough" sleeping conditions.
"Whether that's rough sleeping or tented accommodation and we've got 450 international protection applicants (IPAS) who have arrived into Ireland without accommodation," Mr McCarthy said.
"When the temperature drops to below freezing it adds, not only to the threat [to] life, (but to) the general hardship," he said.
In December the Irish Human Rights and Equality Commission brought proceedings in its own name before the High Court seeking to address what it called "the State's failure to provide for the basic needs, including shelter, of people recently arriving in Ireland and seeking asylum".
It is the first time the commission has used this legal power since its establishment.
Last April the High Court ruled that the State's failure to provide an Afghan asylum with "material reception conditions", including accommodation, shelter, food and basic hygiene, during another accommodation shortage earlier this year, was unlawful.
