Mr Varadkar has said that Ireland may follow other European counties which have recorded their highest numbers of cases in recent weeks, according to the Irish Times.
The highest number of cases previously recorded in a single day in the Republic was of just short of 1,000 cases, at 936 on April 23rd.
It comes as Northern Ireland confirmed record numbers of cases on both Tuesday and again Wednesday of this week, while the UK hit a one-day high of 7,143 infections on Tuesday.
France confirmed a record daily figure of cases last week, while the Netherlands, the Czech Republic and Latvia all saw their highest numbers of infection this week also.
Speaking on RTÉ’s Prime Time programme, Mr Varadkar said case numbers are rising “exponentially” in the country and are currently on course for record highs.
Fear, anxiety, despair
However, he criticised the “over-concentration on the daily case numbers” and said other metrics were important in assessing how the pandemic is progressing, including deaths, hospitalisations, numbers in intensive care and the rate at which the virus was spreading.
Mr Varadkar also said the reveal of daily case numbers was causing unnecessary “fear and anxiety” along with “despair” in the country, and that case numbers were not the main metric to follow.
He added that deaths and hospitalisations were “nowhere near where they were back in April”, although he cautioned that rates of those testing positive and those entering hospital had increased tenfold since the start of July.
Health experts have cautioned that the numbers of Covid-19 cases registered in the spring were likely much higher than official figures as only people with particular symptoms were then tested for the disease.