Schools will reopen next week as planned, despite the rising number of Covid-19 cases among children aged between five and 12.
Taoiseach Micheál Martin said no consideration was being given to extending the mid-term break.
Tánaiste Leo Varadkar separately said of the possibility of an extended half-term or Christmas break: "We're not anywhere near that point yet. And the thing we need to prioritise for kids is school because they've missed enough school already . . . I think we'd need to see a very serious deterioration in the situation before we'd get to that point."
Teachers have called for the resumption of coronavirus contact tracing and testing of asymptomatic primary school pupils.
Pupils who do not show any symptoms after close contact with someone who has Covid-19 have not been required to restrict their movements since late September, when the Government accepted National Public Health Emergency Team (Nphet) recommendations on measures for children aged up to 13 years.
The Irish National Teachers’ Organisation – the main union for primary-level teachers – has demanded a rethink.
Mr Varadkar said Nphet would consider if this needed to be examined again.
He also raised the possibility that rapid antigen tests could be used for children who are close contacts of a case in their classroom pods.
Meanwhile, the Taoiseach, speaking during a visit to University College Dublin, said he supported children continuing outdoor activities and sports, comments that appear to differ from the advice offered by deputy chief medical officer Dr Ronan Glynn.
Dr Glynn suggested on Wednesday that parents should consider limiting their children’s playdates and sport given the high incidence of the virus in the country.
Mr Martin said the Government had received “no specific advice” from Nphet on the issue and its consistent message had been “towards all of us generally just reining it in a bit”.
He said: “I think the more outdoor activities we can continue with, the healthier and the better.”
Asked about the chances of another lockdown Mr Varadkar offered an indication of the thresholds that could lead to renewed restrictions.
He said: “Nobody can rule it out,” but added, “we do believe we can avoid it”.
“Because of the vaccination programme 2,000/3,000 cases a day doesn’t mean what it meant last year or last winter.”
He said the number of people in intensive care units (ICUs) was at about 100 and hospital numbers were about 500 and projections show hospitalisations could increase to “maybe 800”.
“There are more than 800 extra beds in the system than there were before the pandemic and ICU numbers may be going to 150, a bit higher.
“If we can keep it in that space then I don’t think it will be necessary to reimpose restrictions.
“But if it started to go well ahead of those kind of numbers then we would started to get more worried,” Mr Varadkar said.
A further 2,605 new Covid-19 cases were confirmed on Thursday.
