Housing, and the Opposition's proposals for an all-party committee on the future of the health service, are expected to be discussed
The new Cabinet is holding its first full meeting this morning.
They are expected to discuss a number of issues, including priorities for their new departments.
Housing and health are two of the areas likely to be discussed at the meeting.
A cross-party health motion to establish a committee that will plan the future of the health service is to be considered by Fine Gael and Independents.
Enda Kenny is also expected to inform his Cabinet who his selections for junior ministers are.
The Cabinet meeting comes amid the first calls for one of the new ministers to resign.
Former Environment Minister Alan Kelly has said Finian McGrath should step down over the non-payment of water charges.
Minister McGrath - who was appointed the Super Junior Minister for Disability - and Children's Minister Katherine Zappone are expected to update the cabinet on the terms of reference around a commission of investigation into alleged abuse at a foster care home in the South East.
Minister Zaponne says a Commission has been agreed to, but they now need to set out the terms of reference.