The strict rules will remain in effect until September 13 following the reopening of schools. Companies have been told to let employees work from home if possible and people have been told to avoid public transportation.
Mr Martin said at a press conference: “We are absolutely not at a stage where we can return to normalcy.
“We are at another critical moment. “
Mr Martin also urged people to restrict visitors to their homes and said the elderly should limit their contact.
The Taoiseach said the purpose of the new restrictions was to ensure that key parts of the economy keep commerce alive and schools can welcome students back into classrooms.
He insisted the schools would reopen as planned, after the closures in March.
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He said: “We are now seeing several clusters across the country, in people’s homes, in several workplaces and in a number of other social settings.
“Our 14-day cumulative cases per 100,000 population, a key metric reviewed by NPHET, are now 26 – that’s a number of four.
“Our five-day average of new cases is 116 new cases per day and increasing.
“Today the total number of new cases is 190.”
Tuesday’s rise in cases marked the second highest daily jump since early May.
Until the peak of new cases, Ireland had one of the lowest infection rates in Europe for several weeks.
The Irish government has taken one of the most cautious approaches in Europe to tackle the virus.
The reopening of the economy took place at a slower pace than that of many European countries and several restrictions were maintained for longer.
While the number of hospitalizations rose only slightly, only 33 – or 8% – of Ireland’s public intensive care beds were empty on Monday, the Health Service Executive said.