Taoiseach Leo Varadkar has said it is possible Covid-19 was already in Ireland last year.
He said further research and retrospective testing will give a better idea of when the virus arrived in Ireland.
The first case of Covid-19 was confirmed at the end of February but the Taoiseach said it should not be assumed the virus arrived from Italy at that time.
He told the Dail: "We are still learning about this virus. It is noteworthy that initial experts suggest from retrospective testing that the virus was circulating in France as far back as December last year.
"That is before the virus even had a name or a test for it. In some ways this is not surprising.
"France is well connected to China with dozens of flights every day and Ireland is well connected to France.
"Indeed, it is possible that the virus was already in Ireland last year or in January this year."
Mr Varakdar also confirmed pandemic payments will continue beyond June but warned the crisis payments cannot last forever.
The Taoiseach also clashed with Sinn Fein president Mary Lou McDonald after he accused her of being "two-faced".
It came as Ms McDonald warned Mr Varadkar against stopping the Covid-19 payments.
Mr Varadkar said: "I am sorry that deputy McDonald chose to become so party political in her contributions because what she said was so two-faced and so fundamentally dishonest.
"Sinn Fein ministers are on their Facebook site promoting the fact that they hand out food parcels to the poor, reminiscent to me of Donald Trump handing out toilet roll after the hurricane hit the islands in the Caribbean."
Ms McDonald hit back, saying she is "very proud" of the community work Sinn Fein activists do across the Ireland.
"It's not just in the North where people are running meals on wheels and bringing packages to people who are struggling," she added.
A total of 215,000 tests have been carried out since the outbreak of Covid-19.
Over the past week, close to 62,000 tests have been carried out and of these 2,280 were positive, giving a positivity rate of 3.7%.
Mr Varadkar said this is a rate that is continuing to trend downwards.
He added: "65,000 tests have been carried in long-term care residential centres including nursing homes and 540 nursing homes - or 93% of the total who have been tested so far."
During the course of coronavirus pandemic, almost 3,000 people have been taken to hospital. Of these, 78% have made a full recovery.
Mr Varadkar, who unveiled the Government's road map to reopening services and business on Friday, said he is "increasingly confident, though not certain" the Government can proceed with phase one on Monday, May 18.
"Cabinet will make a final decision on that on Friday May 15, following advice from NPHET (National Public Health Emergency Team)," he added.