The Taoiseach has said that the Government's medium-term plan for living with Covid-19 will involve a reduction of social contacts at all levels, even in the home, as that is where the disease is most prevalent.
Micheál Martin said the priority was to keep schools and colleges open and everything would be done to achieve that, including prioritising schools above sports and opening pubs.
Speaking on RTÉ's The Week in Politics, he rejected suggestions that Ireland should adopt herd immunity, saying it did not work.
He said he was concerned about "aggressive" marching in Dublin yesterday against public health measures.
Mr Martin denied that the Government had been too slow to introduce further restrictions in Dublin as suggested by the acting Chief Medical Officer and it would act decisively on Tuesday.
Citing the restrictions imposed last month on Kildare, Laois and Offaly, he said that "we have to learn from what we have done in the past".
The Taoiseach also said Ireland wants to join the EU initiative on international travel and there could be a system where people travelling here from red-listed countries could be tested for the virus in advance.
Sinn Féin's agriculture spokesperson Matt Carthy said public confidence is being eroded by the decisions the Government is taking to deal with Covid-19 and accused it of "double speak and double standards" over the "contradictions that lie at the heart of some of the restrictions".
He said the issue of international travel "is a really good example of where confused messages have been in place" and "a very simple and understandable process" is needed, which should involve people being tested when they arrive at airports and ports and being allowed to go about their business if they test negative.
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On the protest march in Dublin yesterday against the use of face coverings and other Covid related restrictions, Mr Carthy said the organisers were "trying to manipulate ... some very genuine concerns that are happening within our community".
Labour TD Duncan Smith said the rising rates of Covid-19 in Dublin are concerning and are "out of kilter" with the rest of the country and there needs to be clear guidance in the Government's plan on Tuesday.
He described the Government as being "lost at sea" in its messaging and "if we are going to have to live with Covid-19, there needs to be a plan for how every sector of society will be able to live with Covid".
Independent TD Verona Murphy said the responses to cases of Covid-19 need to be looked at on a localised basis.
She said every time there is an increase in cases of the virus, "we talk about lockdown or a partial lockdown".
'Forthright exchange' on Brexit
On Brexit, Mr Martin said there was a forthright exchange of views with British Prime Minister Boris Johnson.
On Mr Johnson's controversial UK Internal Market Bill, published last Wednesday, Mr Martin said the British decision was "unilateral" and there was no heads-up across the system, including to the Irish Government, task force officials or the EU’s chief Brexit negotiator, Michel Barnier.
Mr Martin said Mr Johnson was creating assertions that were in no way associated with reality and a no-deal Brexit would be ruinous for Britain and damaging for the Irish economy.
He said whatever ploy was intended would be met by a very firm and strategic response on the EU side.
"They do care in the end."
Mr Martin said Mr Johnson "knows well" that the European Union is not trying to break up the UK.
Asked about reports of internal tensions within his party, Mr Martin said there was no scathing criticism of him at last week’s Parliamentary Party meeting and one person had spoken at the end of the meeting.
He said he was talking to his TDs and on the doors with them and suggestions he was not engaging with them is "nonsense and rubbish".