Almost a third of passengers arriving at Dublin Airport were still not filling in passenger location forms up to last week.
New figures show almost 3,000 people who arrived from April 28 to May 21 did not say where they would be self-isolating for two weeks.
The vast majority (2,779) of those who did not fill out the form said they were not provided with one by the airline they travelled with.
The Department of Justice figures showed 186 people refused to fill in the form when asked to do so by the Dublin Airport border management unit.
Another 26 people are recorded as having not filled one out because of "language barriers".
Yesterday it became mandatory for passengers to tell authorities where they will be self-isolating for a fortnight after arriving in Ireland.
Those who refuse to fill in the form face six months in prison or a €2,500 fine.
Sinn Fein health spokesperson Louise O'Reilly, who obtained the figures through parliamentary questions, said the Government should have acted sooner on the advice of the National Public Health Emergency Team (Nphet).
"The Nphet recommended that this system be put in place at their meeting on April 3 but it took more than three weeks to be implemented," she said.
"As we reopen the economy and there is increased activity we cannot have this type of time delay again."
Ms O'Reilly said she was disappointed that passengers were refusing to fill out the form given "the seriousness of the health emergency".
However, she welcomed the fact that it is now compulsory for passengers to tell the authorities were they will be staying.
"The Government should move immediately to publish the data about the levels of compliance when the follow-up calls are made," she added.
Gardai now have the power to call to addresses where people say they are self-isolating when they come to Ireland if they believe someone may not have filled out a form accurately.
Meanwhile, it has also emerged that gardai have established a "direct link" with the Nphet to ensure the concerns of the force are heard when Covid-19 measures are being discussed.
In a statement, Garda Representative Association general secretary Pat Ennis said the link was established after he raised concerns about the impact of Nphet recommendations on the "health, welfare and work" of his members.
Mr Ennis said his members were "justifiably angry" at the Nphet's decision to abandon priority testing for them without consulting An Garda Siochana.