Between 1,000 and 3,500 people are arriving into the country every day from overseas, according to the Health Minister.
Stephen Donnelly made the comments during a Dáil debate on mandatory hotel quarantine, which would affect people arriving here from 20 countries deemed high risk.
Opposition parties have savaged the bill for not going far enough, and want it extended to all passengers arriving into the country.
Minister Donnelly said he's concerned at the number of international arrivals at present.
He said: "While travel volumes are significantly depressed compared to the same period last year, there are still approximately 1,000-3,500 arrivals into the country every day.
"Around 10,500 people [arrived] into Dublin Airport just last week."
Multiple parties have submitted amendments to extend the application of mandatory quarantine to all passengers.
People Before Profit TD Richard Boyd Barrett told the Dáil that the Government's approach needs to change.
He said: "You can't live beside COVID-19 - that is a fantasy... a fatal fantasy for more than 1,000 people who have lost their lives lone this year."
Sinn Féin TD David Cullinane was harshly critical of the Government for the lack of detail on the implementation of the quarantine strategy.
He said: "I have no idea if all of the detail has been worked out... in fact I have a good idea that most of it hasn't been worked out.
"There's still a lot of work to be done - and that's nine months after you were told by NPHET to remain the discretionary elements of travel, in relation to testing post-arrival and quarantine."
The legislation around mandatory quarantine is expected to take another few weeks to pass through the Oireachtas.