By Cate McCurry, PA.
The Taoiseach said he would like to be able to accelerate the reopening of the country, but said it is "too soon" to make the call.
As Ireland eased into its first phase on Monday, which saw the opening of some retail stores and sporting activities, the impact on the potential spread of Covid-19 will not be known until early June.
Leo Varadkar said the public's actions have worked as Ireland is reporting a very small number of new Covid-19 cases every day.
"We just need to monitor the situation now over the next two weeks.
"We have the plan, which everyone's familiar with at this stage," he told Newstalk Breakfast radio show.
"I'd like to be in the situation where we can accelerate the opening of the country, but it's far too soon to make that call because we still don't know what the impact is of these restrictions (being removed) that happened this Monday.
"We won't know that really until the first week of June, before we can make any call on moving to phase two, or even perhaps bringing forward some of the relaxations, we'll need see that data first.
"I'd really appeal to people in the meantime to follow that basic common sense that helps us to avoid the virus spreading again.
"If and only if the data says it is safe to do so and we're very much reliant on the CMO (chief medical officer) and NPHET (National Public Health and Emergency Team) to be in charge of the data.
"I am conscious looking at other countries, albeit countries that went into the crisis before we did, that they're opening up, I see in Spain that outdoor terraces and bars are open, wouldn't we all love to have had an opportunity this weekend?"
Mr Varadkar also said he has concerns about secondary deaths as a result of Government decisions to help curb the spread of Covid-19.
He urged the public to seek help if they have chest pain or any symptoms of a stroke.
"We're always very conscious of this whole issue of secondary deaths, people who don't die of Covid but die as a consequence of some of the decisions we have to take to get Covid under control," he added.
"There's delayed diagnosis for cancers, for example.
"It's people not going to hospital when they have chest pain or when they have symptoms of stroke and potentially dying as a result."
Mr Varadkar denied suggestions the current economic crisis is worse than the last financial crash.
He said that some sectors will bounce back quite quickly like construction and retail.
He warned, however, sectors including hospitality, tourism, travel, leisure and entertainment will struggle.
He added: "That's the sector that was hit first and worst, and will be affected for the longest and therefore it's going to be one of the sectors that's going to need the maximum amount of assistance and support.
"Not just not just this year but in the medium term.
"But I do think other sectors you'll see recovering much more.
"I think the airports need to be careful not to lay off too many stuff too quickly because one thing I think is going to be different about aviation in the future, is it's probably going to be more labour intensive.
"Flying in Ireland and in Europe might be a little bit more like people have experienced in East Asia.
"More checks, potentially temperature checks, testing, that type of thing and they require more staff than we would have had for the same number of passengers previously.
"Also it will probably mean more expensive too, unfortunately."
The coronavirus death toll in Ireland rose to 1,571 on Wednesday after a further 11 deaths were announced.
There were 64 new confirmed cases of the infection, bringing the total since the outbreak began in Ireland to 24,315.
It was the fifth day in a row that the daily tally has been below 100.