Minister Simon Harris has praised the "amazing" work of the Irish people by weakening the virus over the last few weeks but has heard of some people breaking the rules.
The Minister for Health said he is feeling “optimistic” about how the country is faring but does have some concerns about house parties and street parties in the last week.
Ireland entered phase one of the reopening roadmap on Monday last but the Minister says it is too early to tell if there will be a jump in cases as a result.
The Minister told Doireann Garrihy on RTE 2fm: “It is too early to say, what happens is there’s a bit of a time lag between lifting in restrictions and a what you would see in your figures so some time later this week we should start to see in our case numbers whether or easing of restrictions has had an impact.
“My sense of it it is we are doing pretty well. I think people are making a real effort.
“On the other hand I am hearing stories of house parties and street parties that are happening, I would appeal to everyone to keep to the measures we are allowed to do.
“We’ve got to see this though, there was one day last month there was 1,068 new cases of Covid-19 in one single day, we’ve had for eight of the last nine days less than 100 cases.
“Quite amazing the effort the Irish people have made and the difference it is having. Absolutely no doubt we are in a better position with this virus.
“But there is always that risk if we get a bit sloppy in terms of how we behave in terms of public health advice we won’t finish the job.”
People looking forward to weddings and other big gatherings after phase five of the reopening have also been warned there is no guarantee life will be back to normal by then.
Ireland’s roadmap ends on August 10th all going well but Harris has stressed life will not be going back to normal.
The Minister said: “What the roadmap does say is that phase five you are allowed to get into larger social gatherings.
“What larger is would depend on how we are dealing with the virus.
“You’d be hopeful by autumn depending where the virus is we would be able to have larger gatherings like weddings again.
“If have to be honest, no one can tell with certainty where this virus will be in a few months.”
Harris has also said that the 2m social distancing rule will be kept under review but at the moment there has been no change.
He added: “We will keep it under review, at the moment the advice is you should keep yourself 2m between you and other people.
“There are different views on this, today it is important to stick to the 2m now because each day that we do it we are making the virus harder to spread.”
He wasn’t drawn on whether Ireland will be good to move into phase two in two weeks but is hopeful that will be the case.
“We can only decide to move forward to each phase if doctors think it is safe to do so.”
