The Taoiseach Micheál Martin has said the the Attorney-General is examining how the movement of people between Ireland and Northern Ireland can be policed.
It comes after the Government announced an extension of level five coronavirus restrictions.
This will include a clampdown on and increased fines associated with non-essential international travel.
Regulations will apply to anyone who travels into the the country from any port or airport on the island - including ports and airports in Northern Ireland.
Mr Martin told The Hard Shoulder that the Government is examining what can be done in terms of cross-border travel.
"The other issue is Northern Ireland and the border, and that has been the big weakness in terms of travel.
"There's an achilles heel there in terms of people in a position to come into the North and travel into the Republic.
"We don't have any checks and so on - what we're now doing is going to make it statutory that you have to obey the same requirements once you come into the Republic as everybody else".
Asked about plans for increased checks between North and South, Mr Martin said: "The Attorney-General's examining that legally with a view to enabling us to deal with that legally, and on a statutory basis, in terms of people coming in from Northern Ireland into the Republic in terms of our capacity to police that as well".
"There's seamless interaction at the border - we are interested in having stronger measures to police traffic, and the Gardaí have been actually doing that."
He said Garda checkpoints "back from the border" - such as on the M1 - will continue.
But he added: "There is a lot of seamless interaction that goes on: people are working both sides of the border, as you know, they travel and so on to work and there has to be a balance there in terms of being conscious of that reality.
"Whilst at the same time, yes, clamping down and creating stronger legal structures on people who will breach our rules here".
He said any approach has to be "grounded in proper legal footing".
He said the majority of people coming back into the country from abroad are Irish citizens.
"The overall advice is not to travel, we're saying to people there's no basis to be travelling abroad unless you've essential work.
"Quite a number of the people who are currently travelling and coming back into the country last week, quite a significant majority were Irish citizens returning from holidays.
"So we're going to step up the extra Garda checkpoints at ports, at airports to check on returning passengers because we want to deter people from non-essential foreign travel".