Adopting a zero Covid strategy is "not realistic or achievable" the Minister for Public Expenditure and Reform has said.
The Government has come under increasing pressure from members of the opposition to switch to a zero Covid plan, similar to Australia and New Zealand.
Dismissing this option, Michael McGrath said the Government is working to "suppress the transmission of the virus" to get the numbers low and then to keep them low.
It comes as the Government announced a raft of new measures to tackle non-essential travel, including mandatory hotel quarantining for some people arriving in Ireland and an increased garda presence at airports as well as along the border.
More than 140 files have been sent to the DPP relating to people who arrived in Ireland without a PCR test, while 1,500 people have been fined for breaching the 5km limit.
The Public Expenditure Minister said the extension of Level 5 restrictions and new measures to combat non-essential travel are being introduced to take pressure off our hospital system
But he warned that "even in a month's time, and hopefully our daily case numbers will be very low, there will still be significant pressure on our frontline healthcare staff."
The Minister said the vast majority of people are compliant with the Covid rules, however, some are not and as a result, the fine for people who take non-essential foreign journeys will increase.
Mr McGrath said: "Enforcement is important, I think, by and large, we have sought to use the power of persuasion and to bring people with us all the way back to March of last year, and I think we've had a lot of success in that regard."
He said travel from Cork airport has slowed down to one route being served by one airline with three flights per week.
Mr McGrath, who was speaking on bothand this morning, said he is still hopeful that the Leaving Cert exams will go ahead, but added that an announcement on this will be made by Education Minister Norma Foley shortly.
"We acknowledge this is an incredibly stressful time for the students, and indeed for their families as well.
"It is the view generally of the stakeholders across the system that we should try to have the Leaving Certificate and that is our aim, we acknowledged that there will be a need in a reasonably short period of time now to give certainty to all involved.
"Minister Foley is working very hard behind the scenes quietly, with the education partners to try to reach an agreement," Mr McGrath said.