Cabinet ministers fear a public backlash over new mandatory quarantine plans which they believe do not go far enough to stop the spread of the virus from overseas.
The new quarantine rules will only apply to anyone travelling from South Africa and Brazil, along with those who arrive in Ireland without a negative Covid-19 test.
All other passengers are to be subject to mandatory quarantine in their homes, while a new €500 fine for taking any non-essential travel is to be introduced.
However, during a more than four-hour Cabinet meeting, ministers raised concerns the quarantine proposals will not go far enough to stop the spread of the virus or appease public demand for tighter controls on our borders once the spread of the disease is brought under control
At the meeting, Culture Minister Catherine Martin and Higher Education Minister Simon Harris both called for stronger regulations than those proposed by the Cabinet Committee on Covid-19.
Ms Martin, the Green Party deputy leader, told the meeting she did not believe the quarantine rules were strong enough to deal with the possibility of more variants of the virus emerging.
She said a larger managed isolation regime was needed and suggested life would return to near normal by the summer if it was introduced.
Mr Harris also said the new rules did not go far enough and called for more clarity on how the proposed quarantine regulations will work in practice.
Chief Whip Jack Chambers and Education Minister Norma Foley also pushed for tighter restrictions on travellers who are to be legally ordered to quarantine in their homes.
Mr Chambers insisted people should be told to remain in their homes for the two weeks rather than be instructed to restrict their movements.
He said the messaging on quarantining at home should be strong to ensure compliance.
His call for stricter rules on mandatory quarantining at home was supported by Ms Foley.
Questions were also raised at the meeting about how mandatory quarantining at home could be policed.
Ministers also called for the list of essential workers to be narrowed to reduce the amount of people allowed to travel overseas.
Sources at the meeting said the quarantine proposals presented to the gathering needed a lot more work which Health Minister Stephen Donnelly committed to undertake in cooperation with other departments.
"I think we are out of step with the public on this and we should be going further," a source said.
Sinn Féin leader Mary Lou McDonald said it was "crazy" to expect that people will quarantine in their homes.
She called for all passengers to be held in quarantine hotels.
Labour Party leader Alan Kelly said the quarantine plans were "half-baked, and will confuse the situation more".
"It was a missed opportunity to once and for all set out a strategy to suppress and contain the virus," he said.
"What we needed was a strong message from the Government that it will once and for all act, instead of more short-term responses, and stop-gap proposals."
Social Democrats co-leader Róisín Shortall said there is public support for stronger restrictions and urged the Government to act faster.
Separately, Housing Minister Darragh O'Brien raised concerns at Cabinet about the impact of the continued ban on non-essential construction.
He told the meeting for every week of the lockdown between 700 and 800 houses will not be built.
He said the nine weeks of lockdown this year mean his housing targets will be off by between 6,500 and 7,000 homes.
The minister made a submission to the Cabinet Committee on Covid-19 over the weekend seeking to have the ban lifted.
However, it was decided to extend the ban until March 5. The proposals on international travel agreed by the Cabinet included a commitment to increase the fines for breaches of the rules.
The Taoiseach said the fines will be €500.
The Government said there will be increased Garda checks and enforcement activity on people making non-essential journeys during Level 5 restrictions.
Green Party leader Eamon Ryan said under new rules being considered gardaí will be able to ask people travelling from the North to the Republic to turn back if their journey is not deemed essential.
Regulations for some of the new rules will be signed this week but new legislation will have to be drafted for other elements of the Government's travel restrictions.