Taoiseach Leo Varadkar has said COVID-19 in the community has been effectively suppressed.
He thanked people for complying with the phase one rules of the re-opening of the country.
Speaking in the Dáil he said: "There has been broad compliance with the five rules and the four steps - so I want to say thank you to the Irish people.
"We have shown our capacity to re-organise our lives to protect the welfare of all, and it is a remarkable demonstration of solidarity and care for each other".
But he said the real effect on the reproductive rate will not be known until the first week in June.
"We need to stay vigilant - we really won't know until the first week of June whether the easing of the restrictions has increased the reproduction number, or to what extent".
He said the Government will make a decision on whether the country can move to phase two on Friday June 5th.
"I know that some other countries are opening faster, but every country's circumstances are different - and we stand over the slow and steady approach.
"If things go well, it can be accelerated - but we simply cannot make that call at the moment".
He says testing and turnaround times are improving, with the Health Service Executive (HSE) now having the capacity to test 15,000 people a day with up to 100,000 per week.
While the average turnaround time, from swab to result, is on target of being between one and three days this week.
He also said the Government is working on plans for a second wave that coincides with flu season in late autumn or winter.
But he said for now, the numbers are positive.
"This week we have seen the lowest number of daily deaths and cases, and the lowest numbers of people in our ICUs, since March.
"While we continue to mourn those who have died, we will never get used to the daily loss of life.
"We take some comfort in the fact the trend's going in the right direction.
"Transmission in the community has been effectively suppressed, which was the strategy from the beginning.
"And we're now working to suppress it in other settings and clusters".
And he said there is no excuse not to be vaccinated for flu this year, with hopefully a bigger uptake.
"This matters now more than ever, as we need to avoid a second wave of COVID-19 coming at the same time as the flu season.
"It's particularly important that uptake by healthcare workers is much better than in the past.
"This pandemic teaches us that there is no excuse not be vaccinated.
"We've experienced a small taste of what the world was like before vaccines - and it hasn't been good".
Additional reporting: Sean Defoe
Main image: Taoiseach Leo Varadkar speaking in the Dáil on COVID-19 measures. Picture by Oireachtas screenshot