Simon Harris is "optimistic" that Ireland can speed up the coronavirus opening roadmap if we stay on the current path.
However, the Minister for Health has warned that case figures later this week will show how the first restrictions lift has worked.
Ireland entered phase one of the roadmap on May 18 and a jump in cases would be reflected by the end of the week.
Minister Harris told RTE's Prime Time: "Yes(phases could be sped up) is the short answer but it depends entirely on the public health advice.
"The signs are encouraging but not to take from the optimism, we've only gone through the first full week of the easing of phase one.
"We won't yet see until later this week the impact of that easing on our cases.
"I'm optimistic though, I think the people of this country have tried so hard and are getting it.
"What I don't want to do is try and look like we are going fast and have to turn back when we have a spike in our deaths or spike in our cases."
The death toll in the Republic now stands at 1,615.
There have been 24,735 people here who have contracted the virus since the outbreak began.
Speaking on Tuesday evening, Dr Tony Holohan, Chief Medical Officer, said: “As of midnight Monday 25 May, 325,795 tests have been carried out. Over the past week, 30,169 tests were carried out and of these 633 were positive, giving a positivity rate of 2.1%.
“NPHET will meet on Thursday 28th May where further consideration will be given to broadening the case definition.”
