Travellers have been reassured they will be able to travel using EU Covid passports and that a helpline established to assist them will be restored.
International travel to the EU and a number of other countries reopened on Monday for those who are fully vaccinated, have negative tests or have recovered from the virus.
However, there have been teething problems, with some prospective holidaymakers saying they have yet to receive their certs.
A helpline set up to help with issues over the EU Digital Covid Certificate and to ask for a recovery cert has also seen heavy traffic and long waits.
Hildegarde Naughton, junior minister at the Department of Transport told the
work was ongoing to restore the helpline and that travellers will not be unduly affected."Today is the reopening of international travel, and there have been issues with the helpline. I can assure you the Government is working very hard to get that system back up and running as quickly as possible.
"This was the number one ask from the aviation sector that we can reopen international travel as safely as possible, adhering to public health guidance."
She said she would continue to work with the aviation sector on reopening and that the Government would continue to support companies.
"I have constant engagement with the airlines and the airports and what we're doing is continuing to assess and review what's needed to support the sector.
"It's one of the hardest-hit sectors as a result of Covid-19. As part of our economic recovery plan, there's specific mention of supports for the aviation sector.
"But their number one ask over the last couple of months was to reopen international travel and to do so as safely as possible so that's what we're endeavouring to do – working with them so that those supports will continue to be assessed."
Ms Naughton said she does not currently foresee any extra measures for those arriving from the UK.
In England, many Covid measures, including mask-wearing, end on Monday, with tens of thousands of daily cases already being seen. Ms Naughton said while this was being constantly reviewed, no measures are being proposed as yet.
"We're going to be constantly working with public health in relation to assessing all measures around international travel.
"Extra measures may need to be put in place but for today, what we're saying if you're fully vaccinated and fully recovered, is you can come here from the UK.
"It really is up to all passengers that you would go on to reopen EU websites to find out what the requirements are of the country you're travelling to and then when you're coming back to Ireland.
"If you've got your digital Covid cert or a recovery cert, obviously there's no need to quarantine but we're asking passengers to give themselves plenty of time now in advance of when they're travelling.
"Many of the checks are going to be on departure at the airport you're departing from. That was the key recommendation from the European Commission, in order to try and minimise the traffic through the airports, right across Europe. So what we have to do is constantly monitor this to make sure that we can reopen the economy and international travel as safely as possible."
The helpline number is 1800 851 504.