Ireland's vaccination programme continues to gather pace and on Friday, the country achieved a record for the number of jabs administered in one day, 52,000.
Health Minister Stephen Donnelly today said it was a time "for hope".
He said the recent lifting of restrictions had not been accompanied by a surge in infection rates.
"What's happening is that as we're opening up, as people are travelling around more, people are still sticking with the basic measures, they are staying outdoors, they're wearing the masks where they need to and they're keeping their distance from people," he told RTE Radio One.
"They're doing the basics and it's having a big effect. And, on top of that, obviously we're vaccinating now several hundred thousand people a week, which helps. So, I am hopeful. I am an optimist."
Mr Donnelly said Monday would be a big day in relation to how the latest relaxations would impact transmission rates. He said the following Monday would also be key, when retail reopens fully.
"If we all continue doing what clearly we have been doing over the last few months, I think we're looking at a really, really positive summer - the kind of summer the country needs," the minister added.
Meanwhile, the Taoiseach has expressed hope that Ireland can look forward to a good summer as he received his first Covid-19 vaccination.
Micheal Martin was given an AstraZeneca jab at the Cork City Hall vaccination centre on Sunday afternoon.
It came ahead of a series of lockdown restrictions lifting across the country on Monday.
A phased reopening of non-essential retail will begin, with click-and-collect services and in-store shopping by appointment allowed and close contact services, such as hairdressers, can resume.
Restrictions on inter-county travel will also lift while some of the limitations on indoor and outdoor meetings will ease.
Many museums, galleries and libraries will be able to reopen and the number of people allowed to attend religious services, including weddings and funerals, will increase to 50.
Speaking to media at Cork City Hall, Mr Martin said: "I think we're making great progress as a country.
"I think people have done extremely well in responding to the various guidelines over the last number of months and the results are that we are emerging from this pandemic.
"We're set to have a good summer if we can keep this progress going and the vaccination is certainly helping in bring down severe illness and bringing down death and hospitalisation, so keep with it and we're making progress."
