Minister for Health Stephen Donnelly has reiterated the advice that there should be no non-essential travel overseas.
There is a real concern about a second wave of Covid-19 if there is a big increase in international travel, he told RTÉ radio’s Morning Ireland.
The international situation is increasingly volatile and the level of cases contracted abroad has increased in the past week, he said.
“We have to look at this and decide what is best for Ireland.” Mr Donnelly pointed out that there were 10 million cases of the virus around the world, one million in the past week.
There were also increases in the US and the city of Leicester was under lockdown.
In France there were 6,000 new cases last week with 5,000 new cases in Portugal and Spain, he added.
Countries that had previously been considered safe could see a spike in cases, he warned.
"In fairness the airlines had taken a lot of steps to comply with European guidelines to minimise the risk of travel, but there was no such thing as zero risk," he said.
The Minister said that he knew it was not an easy decision for a family to cancel their holiday.
On the issue of airbridges, the plan remained that the government would publish a list of airbridges on July 9, but that the list might not say when the airbridges would be activated.
The reality in Europe was much more nuanced, he said and not all countries were taking the same position.
Denmark had effectively closed its borders and “every country was looking at this for themselves.”
Mr Donnelly said there is a fantastic advantage of being an island.
“We have to decide what is best for Ireland. We need to get this right. Caution is a good thing in our approach,” he said.
The National Public Health Emergency Team (NPHET) is expected to brief the government on the 14 day quarantine period for international travellers today.
The briefing follows reports in the Irish Independent that More than half of people arriving in Ireland are not answering calls to check they are self-isolating.
Anyone travelling into Ireland has to fill out a form telling officials where they plan to self-isolate for two weeks, but the quarantine itself isn't mandatory.
The Irish Independent reports that between the end of May and middle of June, calls were made to 684 recent arrivals.
But new figures show just 308 of the calls were answered.
The Health Minister also says the goal is to have every student back to school in August.
Unions and teachers have expressed concerns about new guidelines on social distancing.
Children up to third class will not have to social distance while those from 3rd to 6th class will be asked to keep one metre apart.
Secondary school students will be asked to keep a distance of 2 metres where possible.
Minister Stephen Donnelly says he knows schools have a tough job to see if they can make it work.
Mr Donnelly says it is important "to listen to the stakeholders" and "engage with the officials to find out how we can open up as much as possible."
"The goal obviously is that every student would be able to go back.
"In secondary schools, it is more complex as students are moving to different classrooms," he says.