The Taoiseach has said he cannot guarantee that the 22 October phase of reopening will proceed as planned.
Micheál Martin's comments come as the Department of Health has been notified of 2,066 new coronavirus cases.
He said a decision will be made early next week.
Mr Martin said a presentation from Deputy Chief Medical Officer Dr Ronan Glynn was "serious".
He added that the trajectory of the disease has taken a wrong turn, with a sudden increase in case numbers.
The Taoiseach said the Government wants to see more data and that it will reflect on the situation.
"It's very important that the public at large realise that Covid hasn't gone away," the Taoiseach said.
He said hospital numbers are higher than he would like them to be and this is having an impact.
It was an "alert to all of us to knuckle down, refocus on this virus because it hasn't gone away," Mr Martin added.
The Tánaiste said a decision on whether or not to proceed with the full lifting of restrictions will be made at next Tuesday's Cabinet meeting.
Leo Varadkar told a meeting of the Fine Gael parliamentary party that the Covid-19 metrics are "worrying and going in the wrong direction".
He said that 300,000 adults have not taken the vaccine and while this is a personal choice, "those choices have effects on other people".
The proposed phase of reopening on 22 October is due to see the majority of restrictions lifted, including requirements for physical distancing and mask wearing outdoors and in private indoor settings.
Measures that are to remain in place include isolating while feeling symptoms of Covid-19 and mask wearing in healthcare settings, indoor retail and on public transport.
Concern was expressed at a meeting of the Senior Officials Group on Covid-19 about whether the latest figures on Covid-19 represent a blip or a trend.
Today's meeting included the secretaries general of government departments, Deputy Chief Medical Officer Dr Ronan Glynn and Chair of the NPHET Epidemiological Modelling Advisory Group Professor Philip Nolan.
While no discussion was held about the plan to lift most of the remaining restrictions from 22 October, the National Public Health Emergency Team is to meet next Monday to review the trends and advise Government on how it should best proceed.
There was concern at the meeting about the rise in Covid-19 positivity rates, testing and tracing, and the number of patients in hospital and in intensive care units.
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Earlier, Minister for Foreign Affairs Simon Coveney said Government remained on track to move ahead with the removal of Covid-19 restrictions on 22 October unless "compelling evidence" on rising infection rates suggested that approach should change.
It comes as Minister for Health, Stephen Donnelly, said he is self-isolating after experiencing mild Covid-19 symptoms. A test returned a non-detected result.
Speaking on RTÉ's News at One, Mr Coveney said the Government will listen to the advice of medical and scientific experts in finalising any decision. He said Chief Medical Officer Dr Tony Holohan, senior NPHET members and civil servants are currently assessing the situation in hospitals, ICUs and in the community.
Mr Coveney said the pandemic is not over and "we still have a lot of Covid in the community" and that despite the high level of vaccinations "it does not mean we can let our guard down".
Additional reporting Fergal Bowers, Tommy Meskill