From today people are allowed to travel up to 5 kilometres from home to exercise.
While those who are cocooning are advised that they can go for a short walk if they avoid all contact with others.
Ireland will then begin to reopen on May 18 and will continue in five three-week phases.
A further 16 deaths from Covid-19 were reported in the Republic yesterday, along with 266 new cases.
1,319 people with Covid 19 have now died in Ireland, and there are a total of 21,772 people with confirmed cases of the virus,
In Mayo the number of confirmed cases of Covid 19 is now more than 500.
There are 501 confirmed cases of Covid 19 in the county, compared to 365 in county Galway, 174 in county Roscommon and in county Sligo 119.
In good news over the weekend, a Mayo grandmother whose weather reading played a critical role on D-Day has beaten Covid-19 at the age of 97.
Maureen Sweeney was 21 years old when she took weather readings at Blacksod weather station in June 1944. Her actions influenced the D-Day landings and changed the course of World War II.
Maureen has been a resident in Tí Aire Nursing Home in Belmullet for the past year. She contracted the coronavirus a number of weeks ago but Maureen received the good news late last week that a re-test had come back negative.