Air travel restrictions, which are set to be eased by the second week of July, will still apply to passengers arriving from Britain.
Ministers decided to exclude Britain's plan to join 'air bridges' with other European countries despite fears it could impact on diplomatic relationships.
In a memo given to a Cabinet sub-committee on the Covid-19 crisis, ministers were told it is "highly unlikely" Britain will be included in an approved list of countries which are safe for foreign travel.
This was because Britain's attempt to tackle the virus has been "significantly poorer" compared to Ireland.
The memo said Britain has "raised concerns" over the restrictions imposed on its citizens flying into Ireland.
"Applications 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.
Ireland was excluded from Britain's quarantine rules for foreign travellers.
Meanwhile, the Government is set to make it mandatory to wear a face mask or covering on public transport in the coming weeks.
Transport Minister Shane Ross will bring a memo to Cabinet making it compulsory to cover your face 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 covering your face while in public settings.
The Cabinet is set to also sign off on the 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 foreign holidays to countries that are deemed to be safe for travel.
However, 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.
It will also "draw on" the Commission's approach for determining the success of a member state with the virus.
"However, it is proposed that, at least initially, Ireland should adopt a more gradual, cautious approach in identifying comparable countries," it added.