The Office of the Refugee Applications Commissioner has postponed the processing of applications, except for Syrian applicants, until new legislation comes into effect at the end of the month.
Under the new laws there will be a single application procedure, which aims to speed up the asylum process.
The current system is fragmented and has been blamed for chronic delays in the asylum process.
Ireland has been criticised in the past for being the only member state in the European Union that does not have a single application procedure.
An estimated 3,000 people have been affected by the postponement of applications - half of which are appeals cases.
The number of refugees resettled to Ireland doubled between 2015 and 2016, according to a new report by the Economic and Social Research Institute.
However, the ESRI says the overall number resettled remains low - both in the context of the refugee crisis and compared to some other countries in Europe.
Ireland pledged to take in 520 refugees under the EU resettlement programme - almost double the number proposed by the European Commission - and as of last month had reached 98% of this total, ahead of schedule.
The majority of refugees who have been resettled in Ireland are of Syrian origin.
The Crossing tells the story of life on board the LÉ Samuel Beckett on its humanitarian mission in the Mediterranean, where thousands of people make the perilous journey crossing into Europe from northern Africa.
Almost 4,000 people have died trying to make the crossing in 2016 alone - more than in any other year.
