The Minister for Health said that he and the acting chief medical officer are “cautiously optimistic” that the tighter restrictions in Dublin are working.
Stephen Donnelly said the vast majority of people in Dublin are following the public health restrictions put in place to curb the spread of Covid-19.
Dublin and Donegal are currently subject to Level Three restrictions under the Government’s Covid-19 five-tier response plan, with the rest of the country at Level 2.
The stricter measures in place in the capital include a ban on indoor social gatherings; a requirement for pubs and restaurants to only serve food outdoors, while travel in and out of the county has been limited to work, education and essential purposes.
Mr Donnelly said public health experts tracking the spread of Covid-19 in Ireland need the seven-day rate of the virus to be less than half of the 14-day rate.
Dublin’s 14-day incidence rate is 147 positive cases per 100,000 population, while its seven-day rate is 78.
“What we want to start seeing is the seven-day rate becomes less than half of the 14-day rate and that shows that it is plateauing,” Mr Donnelly told RTE.
“The chief medical officer (Dr Ronan Glynn) and I have have been speaking on exactly this point over the weekend, we will be cautiously optimistic as we must always be, but it is very early days.
“We want to see that seven-day rate come down each and every day.
“I have no doubt the people of Dublin have heard this loud and clear, and in the vast majority of cases people are doing what they are supposed to do, limiting their interactions.”
He urged the public to halve the number of social contacts they have in a bid to reduce the R number, which is the number of people an infected person will pass the virus on to.
Mr Donnelly said there are no plans for the National Public Health Emergency Team (Nphet) to call an emergency meeting this week, however he warned that could change.
“There are four counties which are being looked at very carefully and they are Cork, Galway, Louth and Wicklow,” he added.
On Sunday an additional 430 cases of Covid-19 were confirmed, the National Public Health Emergency Team (Nphet) said.
There were no further deaths due to the virus, health officials confirmed.
Dr Glynn urged households to reduce their contacts.
He said: “As we start into this new week, I am asking every household across the country to sit together this evening and make a plan to reduce the number of people you meet this week.
“We have absolutely no room for complacency. If every person, family, workplace and organisation does not play their part the situation will continue to deteriorate.
“For people who live in Donegal and Dublin remember Government advice is to work from home unless it is essential to attend in person.
“For people living in these and all other counties, assume that Covid-19 is circulating in your community and act accordingly.”
Earlier on Sunday Mary Lou McDonald warned the cut in the pandemic unemployment payment (PUP) will lead to economic hardship.
The Sinn Féin leader called for the Government to reverse the reduction.
The €350-a-week payments have dropped to between €200 and €300, which has affected the 150,000 people still in receipt of the benefit.
Ms McDonald said that Minister for Finance Paschal Donohoe will have to reverse the decision, saying it was wrong to cut the payment particularly when Dublin and Donegal are facing tighter restrictions.
“I think he will have to change his mind because they’ve made a mistake, because what they’re doing is unfair, because what they’re doing will undoubtedly cause not just hardship, but what MABS (Money Advice and Budgeting Service) has described as a forthcoming tsunami of domestic debt,” she told RTE’s The Week In Politics.
“That’s not a smart thing to do socially or economically so Paschal will have to change his position because it’s the wrong position.”
Ms McDonald rejected Mr Donohoe’s claim that the Government cut the Covid-19 unemployment payments so the PUP could last longer for people.
“I think the very reason to extend and to maintain the payments is the fact that we are still in the grips of a crisis,” she added.
“If we thought initially six months ago that this was a transient crisis, that we could tough it out for six months and then we could go all come back up and breathe air that’s wrong.”
Taoiseach Micheál Martin last week defended the decision saying that, while the rates have been reduced, the scheme had been extended until next April.
Meanwhile, it has emerged that bookings for hotels across Ireland plummeted by 67% in recent weeks, prompting a call by industry leaders for urgent action.
The latest survey from the Irish Hotels Federation (IHF) reveals a collapse in hotel bookings following the tightening of Covid-19 restrictions in Dublin.
The IHF said that after the Government announced its medium-term six-month plan for living with coronavirus, the weekly rate of new bookings declined sharply.
IHF president Elaina Fitzgerald Kane said: “It is now ‘make or break’ time.
“Urgent and unprecedented intervention from the Government is required to support tourism businesses and safeguard thousands of jobs throughout the sector,” she said.
“This must form a central plank of the Budget due to be announced next month.”