Air travel restrictions, which are to be eased by the second week of July, will still apply to passengers arriving from Britain.
Ministers decided to exclude Britain from the plan to join ‘air bridges’ with other European countries, despite fears it could affect diplomatic relationships.
In a memo given to a Cabinet sub-committee on Covid-19, ministers were told it is “highly unlikely” Britain will be included in an approved list of countries safe for foreign travel – which means those arriving from Britain must still undergo a 14-day quarantine period.
This is because Britain’s attempt to tackle the virus has been “significantly poorer” than Ireland’s.
The memo said Britain has “raised concerns” over the restrictions on those flying into Ireland.
“Application of further restrictions by Ireland to travel from Britain will add to those concerns, and may be seen as a unilateral suspension of the Common Travel Area by us,” it added.
Meanwhile, face masks are set to become compulsory on public transport.
Transport Minister Shane Ross will bring a memo to Cabinet making it compulsory for passengers to cover their faces when travelling on buses and trains.
The move follows increasing concerns about the lack of compliance among commuters and shoppers with public health guidance on wearing face coverings in public settings.
The Cabinet is also to sign off on plans to begin easing air travel restrictions by the second week of July.
After a lengthy Cabinet sub-committee yesterday it was agreed Ireland should enter so-called "air bridge" arrangements with other EU countries that have had similar or better success in tackling the virus.
This will clear the way for summer holidays to countries that are deemed safe to travel to.
However, Britain will not have restrictions lifted, despite the fact that Ireland is excluded from Britain's quarantine rules for foreign travellers.
Concerns were expressed at the meeting over an increase in cases of the virus in Ireland from people who have travelled overseas.
It was also noted there have been spikes in a number of EU countries where restrictions have been lifted.
The Cabinet sub-committee memo said Ireland's approach to easing restrictions will be "partially based" on the EU approach, and will "draw on" the European Commission's approach for determining the success of a member state in tackling the virus.
"However, it is proposed that, at least initially, Ireland should adopt a more gradual, cautious approach in identifying comparable or 'approved' countries," it adds.
The memo says restrictions will continue to apply to travel from countries not deemed safe and "mandatory restricted movement" will be introduced.
The Government also plans to introduce temperature testing, diagnostic testing and improved contact tracing to "identify potential cases of the virus and limit any travel-related spread".
It comes as the Dáil's Special Committee on Covid-19 Response will today be warned a resurgence of the virus is "inevitable" as more air travel is permitted.
Prof Paddy Mallon of the UCD School of Medicine will tell TDs there is ongoing community transmission in the US, Sweden and parts of the UK and there has also been a resurgence of cases in Portugal and outbreaks in Germany.
His statement to the committee says this highlights how "Ireland is still very much within a geographical high-risk zone for Covid-19".
Prof Mallon adds: "I and others in the infectious diseases clinical community believe it is inevitable that we will experience a resurgence of cases as we relax restrictions and permit more travel."
Prof Mallon says that, in this context, a "highly effective programme of rapid testing, contact tracing and community actions becomes a priority in maintaining our national biosecurity".
He will warn that despite the "optimism" of recent weeks, "we are still in the midst of a national health emergency and our citizens are at no less risk of severe illness and death if they contract Covid-19 infection now than they were back in March".
Prof Mallon says lessons learned must be translated into actions and resources "but we have a very narrow window of opportunity".
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