However, from Tuesday people will be allowed to exercise within a 5km distance of their homes instead of the current 2km travel limit, and self-isolating over-70s will be able to go for a walk or a drive.
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Addressing the nation from Dublin, Mr Varadkar said that “on the 18th of May, Ireland begins to reopen and begins that journey to a new normal.”
The five stages will be spaced three weeks apart, with the final phase set to begin on 10 August.
The first phase will allow outdoor workers to return to work and for some retail outlets such as garden centres to reopen.
The Taoiseach said that some sporting and fitness activities in small groups would be permitted from 18 May, adding that people could meet up to four friends and family from other households outside while maintaining social distancing.
Visits to the homes of over-70s and other vulnerable groups will be allowed from phase two (8 June), as long as strict social distancing and hygiene steps are adhered to.
Pubs are not due to reopen until the final phase in August, while cafes and restaurants will reopen from the end of June.
Schools will reopen for the start of the new academic year in September/October.
The Cabinet agreed to the plans after medical experts from the National Public Health Emergency Team (Nphet) advised the government on Friday.
Mr Varadkar said that two more weeks of “tight restrictions” were necessary to “weaken the virus further”, cautioning that “we have not yet won this fight”.
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He acknowledged the acute difficulties of lockdown, saying: "I know it has been difficult – sometimes dispiriting.”
"As a nation our physical health has been attacked, our mental health eroded, our economy battered, and our society put to the ultimate test,” he added.
In his address, Mr Varadkar also read out a few of the 10,000 pieces of correspondence that have been sent to him from members of the public since the crisis started.
Speaking of stories of loss and hardship, he said they form a "tapestry of struggle and sacrifice and sorrow".
The Taoiseach added that the country would have to return to tighter restrictions if the virus surged again.
Mr Varadkar and the Cabinet will meet on Saturday to agree further actions to help businesses and their staff.
As of Friday, 1,265 people have died from Covid-19 in Ireland and there have been 20,833 confirmed cases.