The Minister for the Environment has suggested that the current 5km limit on exercise could be reduced to 2km if current restrictions do not lead to a sufficient drop in coronavirus cases.
Eamon Ryan said we will have to "wait and see" if the current level five measures work in slowing the spread of the virus.
The restrictions are currently in place until January 31st.
However, the HSE's Chief Clinical Officer is warning there could be up to 3,000 COVID-19 hospital admissions by the end of the month if the current growth rate continues.
Minister Ryan said the recent figures show a "sobering rise" in the transmission of the virus amid record numbers this week.
Speaking to Seán Defoe on On the Record with Gavan Reilly, he said he expects the figures in the coming week to continue to be very high due to a backlog in the system.
He added that "a really strong effort in the next week from everyone can stop hospitals becoming overrun".
On the next moves which can be taken if the current restrictions do not lead to a sufficient decrease in cases by the end of January, Minister Ryan said there are "always" more which can be done and "it is in our hands" based on "the level of contacts we have".
"Whether that's, for example, reducing the travel restrictions from 5km down to 2km which we did last March and April and a range of different measures that you could look at then," he said.
"That's for a week or two's time if we find that the numbers aren't starting to flatten off and then decrease.
He said that looking at traffic volumes and hearing from friends anecdotally around the country, Irish people are "very aware of the risk that's at stake" and he believes that the population collectively can be good this week in "hunkering down" and adhering to guidelines.
The Green Party leader added that the situation with regard to the reopening schools will be reviewed this week.
However, Minister Ryan said the plan remains that they will welcome back students on January 11th.
It comes amid increasing concern about the rising rate of COVID-19 infections among school-age children.
Senior public health officials, Department of Education officials and teachers unions are due to meet on Wednesday to discuss the issue.
Minister Ryan advised that parents should operate with the view that schools will open again from tomorrow week.
"It is something we have to review and look at but the evidence and I think the public health advice on this is yes, we should be able to do it," he said.
"What we're doing here is two goals, one is to protect our health system and life and secondly, to protect our young people's future and get them back to school.
"If we act collectively and all say at home for the next week which we can do, then I believe it's safe for our schools to reopen."
The Minister added that the Government would be mentoring the situation "every day", with the next week or two "a critical period".
As a random, albeit small, selection of cases primarily from the community, these data would suggest that the #SARSCoV2 #UKvariant - at a proportion of <10% - is not responsible for the recent significant & concerning increase in #SARSCoV2 case numbers #Surveillance #StayAtHome
— Cillian De Gascun (@CillianDeGascun) January 1, 2021
He said that the recent surge in coronavirus cases can "undoubtedly" be attributed to increased contacts and socialisation over the Christmas period.
Additionally, we won't know whether the source of the rise can also be connected to a new variant of COVID-19 until more research is conducted, he said.
The Director of the National Virus Reference Laboratory in UCD, Dr Cillian De Gascun, reported that testing on a small proportion of cases suggests the variant is not responsible for the recent surge in case numbers.
Minister Ryan said: "What combination of those different factors caused the recent spike, we'll have to wait for science to do the full analysis, it's not available yet.
"But I think we're right to be cautious, we know that new variant is here, we know that the science seems to be indicating that it is significantly more transmissible and that therefore makes sense for us to be aware of it and take into account in whatever we're doing."