A security analyst said that further regulation is necessary to enforce self-isolation protocols at airports for returning and international travellers.
Declan Power says news that the Department of Justice is reviewing its regulations for travellers entering Ireland is welcome.
He says: "If you are going to have a regulation you have to have the legal instruments to enforce it.
"There is no point in just asking people questions, and if they refuse to answer them just moving on to the next person, it defeats the purpose."
The Department of Justice says follow-up calls are made a number of days after people arrive here.
Between April 28 and May 1, 637 calls were made and two-thirds of people picked up.
99% of passengers who answered confirmed they were self-isolating.
There are calls for tougher laws to be introduced to force people to tell immigration officials at the country's airports where they will be self-isolating.
Under new Covid-19 rules, anyone arriving in Ireland is asked to sign a passenger location form when they arrive.
But a third of passengers who flew to Dublin Airport over the past six weeks failed to do so, according to the Irish Independent.
Fianna Fáil's transport spokesman, Marc MacSharry, says stricter enforcement is needed.
He says: "Certainly, clearly there is a gap in the resources that are available to authorities at the airport if people are refusing or through wilful neglect not making the appropriate declarations they need to.
"It is certainly a matter we will raise with the Minister for Transport and if there are additional powers needed for these people then we will certainly be pushing for that to happen."
A third of people arriving in Ireland over the past six weeks refused to give details of where they would be self-isolating.
The Irish Independent says hundreds of people who flew into Dublin Airport did not fill in forms detailing where they would be staying.
The forms asked for information about the address where the person would stay for two weeks after they arrived.
Anyone arriving in Ireland is asked to sign a passenger location form when they arrive at the airport, to stop the spread of Covid-19.
The news comes as just 2% of the individuals trained as contact tracers in the fight against Covid-19 are currently employed to that end.
As of Tuesday of this week, just 40 of roughly 2,000 people trained to track the coronavirus via those it has infected were doing so.
The low level of contact tracing being employed was criticised by Peadar Toibin, TD and leader of Aontu, as being emblematic of “the mismatch between capacity and need” in the Irish health service.