More than 1,300 people have refused a Covid-19 test despite being at risk of the killer disease after being in close contact with an infected person.
The figure showing 1,314 have snubbed the offer was revealed by the HSE to the Special Committee on Covid-19 Response.
National clinical director for health protection Dr Lorraine Doherty said the HSE was concerned about people not turning up for tests.
"It shows the public are becoming disengaged with the idea of having a Covid-19 test if they are symptomatic or if they are a contact because they understand the implications of having a test and that they would need to restrict their movements," she said.
"For people in workplaces, they might be reluctant to be tested.
"However, our public health messaging is very clear - you should have a test if you are symptomatic or in contact with someone who is symptomatic."
Fine Gael TD Fergus O' Dowd said: "The gardai may need to call to people's doors if they refuse to come for a Covid-19 test."
It comes as 36 more people were diagnosed with the virus yesterday, confirming an on- going high level of new infections.
There were no deaths from the virus, the sixth day in the past 10 days when no fatalities have been reported.
The number of patients in intensive care remains low at seven.
Acting Chief Medical Officer Dr Ronan Glynn said: "Today I am asking everyone to stay the course on the public health measures needed to suppress Covid-19, such as covering coughs, handwashing, use of face coverings and two-metre social-distancing, which are essential for continuing the momentum toward the re- opening of our schools and the resumption of our healthcare services."
The HSE also indicated yesterday that it will reduce the two-metre rule in some settings to facilitate health services.
Meanwhile, a stark insight into poor infection control in many Covid-hit nursing homes, where the doors of infected residents' rooms were left open and staff suggested a "neighbour might do the laundry", was revealed in a report yesterday.
Half of all people who have died from the virus in Ireland were residents of nursing homes, and the report, based on inspections by the Health Information and Quality Authority (Hiqa), shows how many homes were ill-equipped to deal with the threat.
In one case, chief inspector Mary Dunnion was so concerned about the ability of one outbreak-hit nursing home to care for 16 residents that there was an emergency court order to close it down on May 30.
The report shows that of the 44 homes inspected since May, most failed to fully meet regulations and six in 10 were in breach of governance and management standards.
The findings revealed:
Covid-19 has brought into sharp focus the need for reform of current models of care for older people.
Ms Dunnion said: "We must look to complementary models of care, such as homecare and assisted living, and ensure that there is improved clinical oversight in all nursing homes."