The Health Minister says the "big risk" of a spike in coronavirus cases comes from international travel.
The government has committed to publishing a list of countries where Irish people can travel to without having to quarantine when they come back.
Last Thursday, the previous government announced that foreign travel to certain countries from July 9 has been approved.
Air bridges will be established between countries with similarly low infection rates from that date, enabling people to travel without undergoing quarantine.
Stephen Donnelly - who yesterday was made the Minister for Health - says there is a risk associated with more people travelling.
“The great advantage we have as an island, obviously, is we have a natural border.
“So if we can continue to do everything we can to ideally eliminate this virus on the island, but certainly to bring it down to a very very low level, then obviously the big risk is international travel.”
Mr Donnelly said there is no commitment yet to when a list of countries Irish people can travel to without quarantining on their return will be published.
Earlier this week, Chief Medical Officer Tony Holohan said that he was worried about the prospect of international travel resuming.
“We are beyond nervous. We are concerned about travel as a potential source of infection for this country,” he said.
“If there are countries that have verifiable information that tells us that they are either below the threshold that makes sense ... then we can contemplate those arrangements.”
The CMO has advised people that this year, holidays should be about "staycations”.
Writing on Twitter as the country prepares to move into Phase Three of reopening society, he said: "What worries me most now is travel from overseas and I fear many planning foreign trips.
"2020 is a year for a staycation. Stay in Ireland, spend locally and follow public health advice."
Meanwhile, the number of new travel-related Covid-19 cases is a “grave concern”, Professor Philip Nolan has said.
Professor Nolan, chairman of the National Public Health Emergency Team Irish epidemiological modelling advisory group, said people should question whether they need to take a foreign holiday this year due to the risk of a resurgence of the virus.
He tweeted: “New travel-related Covid-19 infections a grave concern. A surge seeded by travel is a risk to public health, to healthcare workers, to the vulnerable in our community. We can protect them by foregoing our holiday abroad. A useful question for any activity: luxury or necessity?”
