The Department of Integration has confirmed that 76 asylum seekers remain without State-provided accommodation.
In total, since Monday, the service has had to turn away 83 people, however seven places were provided retrospectively.
On Tuesday, the Cabinet decided to increase by €75 the weekly payments for asylum seekers who are not offered accommodation.
In total they will be provided with €113.50 per week for as long as they are left without accommodation.
Separately, it is expected that the a Cabinet sub-committee will discuss on Monday proposals to change how Ukrainian refugees are accommodated in Ireland.
Possible changes include a proposal that new arrivals would spend 90 days in State-provided accommodation after which they would have to find a place to live.