The Cabinet is also expected to agree to a rise in rent supplement
The Transport Minister Shane Ross says Taoiseach Enda Kenny will have to take a strong position over how the Brexit vote will threaten Irish interests when he meets with his counterparts in Brussels later.
Minister Ross says Ireland is probably in the worst position of any country, as a result of Britain's vote to leave the European Union.
The issue of when the United Kingdom will trigger the mechanism to leave the union is expected to be the main issue discussed when the 27 EU leaders meet with the British Prime Minister David Cameron later.
Mr Ross says the Taoiseach will need to keep his composure at the meeting.
The Brexit, a rise in rent allowance and re-opening rural garda stations are on the agenda for the Cabinet meeting.
The Cabinet meeting began early this morning to allow Mr Kenny to travel to Brussels for a crisis meeting of EU states.
Ministers are discussing the possible fallout for Ireland from the leave vote.
A move aimed at tackling homelessness is also being discussed.
The Cabinet is expected to agree to a rise in rent supplement and housing assistance payments, which will kick in next week.
The Justice Minister Frances Fitzgerald is also bringing forward a proposal to open some of the closed garda stations on a trial basis.
Six stations will be re-opened and monitored to see if they have an impact on local crime levels.
Also on the agenda is Mick Wallace's abortion bill, which would see terminations allowed in cases of fatal foetal abnormality.
The Cabinet will receive legal advice on whether the bill is constitutional.