There have been Covid-19 outbreaks linked to at least three flights into Ireland in the past fortnight, according to a spokesperson from the Department of Health.
The spokesperson said two of these outbreaks involve possible variants of concern and are still being investigated.
The department has defended the rules requiring people arriving from designated countries, who are fully vaccinated, to quarantine in a hotel.
A spokesperson said there is some evidence that individuals who have already been vaccinated have subsequently been diagnosed with a variant of concern.
The department also argued that there is no international system that recognises vaccination certificates and no agreed method that could allow people to prove they are vaccinated.
On the question of why quarantine rules must apply to those transiting through countries on the mandatory hotel quarantine list, the spokesperson said there have been several cases of in-flight transmission during the pandemic.
One flight resulted in onward transmission with 59 cases across six HSE regions.
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With all primary and secondary students returning to schools tomorrow, Bus Éireann is advising passengers "to plan their essential journeys and to be aware of the continuing 25% capacity limit on all public transport".
In a statement, the bus company said that as schools return "some city and town services may see an increase in demand on morning and afternoon services".
"Public transport remains at 25% capacity and therefore should only be used for essential journeys," said Chief Customer Officer Allen Parker.
Meanwhile, the HSE clinical lead on infection control has said that while progress has been made in battling Covid-19, "we still have to be careful for some time yet".
Professor Martin Cormican told RTÉ's This Week: "Case numbers are still much higher than what we saw last summer. We are going to have to go forward in small steps."
He said "around 25%" of positive cases are undergoing genomic sequence testing and "that is enough to give a very good representation of what is going on".
Prof Cormican said 19 cases of the P1 variant (that originated in Brazil) had been found in Ireland so far, but said the spread has been "very limited because people took the necessary precautions".
Earlier, public health expert Professor Anthony Staines said he did not think that life will return to "relative normality" until the autumn, when "most people will have had two doses of vaccines. It is going to take that long".
He said that "people underestimate how infectious" coronavirus is.