'The Government must draw a line under the shambles over the Green list and concerns about unregulated quarantine for visitors here,' said Labour Transport spokesperson and local TD, Duncan Smith.
He called on the government to publish a clear definition of essential travel, the public health advice they received, along with clear communications now on the rules covering international travel.
Deputy Smith said: 'The Cabinet decision last week brought some clarity to the shambles we've seen over international travel but it still doesn't address the concerns people have over travel.
'Everyone knows that green means go. However we've had a fortnight of mixed messages about international travel into and out of our island.
'We still have no definition of essential travel and the criteria that apply for Irish people who have bookings for holidays in Green list locations is not clear. If they cancel their holiday can they get a refund? The Government should also publish the public health advice they relied on for their decision.
'The mixed messages must now stop, and the Cabinet decision is the first step to address that. However more needs to be done. I've called for a number of clear measures that would reassure the public and address concerns as the rules we've had to date are unworkable and unenforceable. Specifically I called for testing of visitors from Covid-19 hotspots more than a week ago and in person follow up with those who are meant to be in quarantine in 14 days. Sadly that was not announced last night.'
Fine Gael TD for Dublin Fingal, Alan Farrell, has urged the public not to engage in international travel, despite the publication of the 'Green-List'.
Deputy Farrell said: 'The continued message from the Government is that non-essential travel should be avoided by all people living in Ireland.
'However, we know that approximately 50,000 people are traveling each week from Ireland, some of these people are indeed travelling for essential reasons but some are not.
'The 'Green List' has been published in light of this reality. The Green List reflects the countries that have the same rate, or lower, of infection over the past 14 days.
'Countries that are not on the list are deemed to have a higher risk than that of the risk presently posed in Ireland.'
Deputy Farrell continued, 'This list is not a license to travel to these countries and should not be seen as an encouragement to do so, but it is a way of reducing the possible risks if international travel is to take place.
'We are in a critical phase in our battle against Covid-19, through the hard-work and sacrifice of the Irish people, we managed to flatten the curve and save thousands of lives.
'We have asked a lot of our people and it is natural that as we reopen our society there are temptations to become complacent, however, we must not give in now.'