The Government has agreed on a list of 15 countries where people can travel without being asked to quarantines on their return.
But after a lengthy Cabinet meeting, the Government is still advising to people not to travel abroad unless it is an essential journey.
The countries on the much-anticipated 'green list' where it is deemed safe to travel are Malta, Finland, Norway, Italy, Hungary, Estonia, Latvia, Lithuania, Cyprus, Slovakia, Greece, Greenland, Gibraltar, Monaco and San Marino.
People travelling from Ireland to these countries are advised to take "normal precautions".
Travellers from the 15 countries will be exempt from the two-week quarantine expected of all passengers arriving in Dublin Airport.
The list will be reviewed in two weeks.
The Government also agreed on new protocols which will see random testing of passengers arriving in Ireland from high-risk countries.
Earlier yesterday, Tánaiste Leo Varadkar suggested the green list should be ditched if people are still being told not to travel abroad.
However, as it published the list last night, the Government's message was still "the safest thing to do is not travel abroad so please holiday at home this summer".
Mr Varadkar issued a statement criticising "mixed messages" around Government plans to ease travel restrictions for countries with similar levels of Covid-19.
The Tánaiste's spokesperson said Mr Varadkar "believes strongly that it's wrong to send out mixed messages about international travel".
"The Tánaiste believes there should be a green list as was previously agreed by Government.
"But if the travel advice for countries on the green list isn't different to advice for other countries, then we would be better off not having a green list at all," he added.
Mr Varadkar's intervention prompted Labour leader Alan Kelly to tell Mr Martin in the Dáil: "I'm beginning to wonder who's the Taoiseach."
Under Mr Varadkar's government it was proposed that so-called "air bridges" be created between Ireland and countries designated safe for travel on the green list.
This would mean people living in Ireland could travel to and from these destinations without the need to quarantine for two weeks in either country.
People travelling to countries on the green list will be able to avoid self-isolating on their return.
However, the Government said some of those arriving from high-risk countries will be subject to random testing.
Anyone entering the country with symptoms of the coronavirus will be tested and they will be given accommodation while awaiting their results.
However, Mr Martin and Health Minister Stephen Donnelly are eager to discourage people from making any non-essential journeys following a spike in the number of new cases here.
In the Dáil, Mr Kelly challenged the Taoiseach on why Covid-19 tests aren't being carried out at airports when people arrive.
Referring to Mr Varadkar's statement, he also said: "I'm beginning to wonder who's the Taoiseach."
He said Mr Martin and other ministers had suggested a green list would be published yesterday.
He added that Mr Varadkar said that due to mixed messages he didn't see the point of a green list being published.
"So which is it? Is it what you say in here or is it what he says outside?"
Mr Martin responded by saying the Government was going to decide on the matter yesterday evening.
He said the green list had previously been postponed.
Mr Martin said the challenge is living with Covid-19 and "getting the balance right", adding: "The Government will decide on that."
He said the National Public Health Emergency Team was not in favour of systematic testing at airports.
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