The number of recently arrived asylum seekers without State provided accommodation has fallen below 100 for the first time since February.
The latest figures from the Department of Integration show that there are now 74 recently arrived adult asylum seekers with no State provided accommodation.
In the last 24 hours 100 people who did not have any accommodation were offered a space, while 50 were offered a place the day before.
Some 14 new arrivals who presented today were not offered any accommodation.
Since 24 January, 1,301 asylum seekers who were initially told there was no accommodation available for them have been offered a space.
Last month the number of asylum seekers without any State provided accommodation peaked, when on the evening of the 3 May there were a total of 593 without accommodation.
Earlier this week a senior official in the Department of Integration warned that accommodation for adult asylum seekers presenting without children will remain "strained" into the future.
Ms Baxter acknowledged that the State has "a legal and moral obligation to access the claims of those who seek refuge and to provide accommodation and supports in line with the (European Union) Reception Conditions Directive."
Independent Senator Tom Clonan said he believed the situation was an emergency rather than a crisis and suggested that tents sheltering homeless asylum seekers on streets could be moved to army barracks already in use including McKee and Cathal Brugha barracks in Dublin.
Read more: Three new accommodation centres for asylum seekers to open in Dublin