© DMG Media Ireland
Fine Gael TD Fergus O'Dowd told the Dail Covid-19 committee 1,314 people who are a direct contact of a person who has a confirmed case of Covid-19, have not turned up for a test.
"That seems like a very high figure to me," he told the committee.
O'Dowd said could call to their homes and ask them to take a test as it is a serious public health issue.
He said: "I think it is a huge figure and you need to do more work on it. If it means that the Gardai (may need to) call to them.. You know who these people are - it is not a question that they are unknown.
"They are known people and you have their home addresses. I think they (the Gardaí) should call and tell them that in the public health interest they should turn up for a test."
© Press AssociationFergus O'Dowd speaking at the Dáil Covid-19 committee
"That's very serious because you could theoretically have it and give it to many, many more people."
Dr Lorraine Doherty, HSE National clinical director for Health Protection said they are concerned about people not turning up for tests.
She said: "It shows that 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."
"For people in workplaces, they might be reluctant to be tested.
However our public health messaging is very clear, you should have test if you are symptomatic or in contact with someone who is symptomatic.She said contact-tracing staff make every effort to reach people who need to come for a Covid-19 test.
"I want to reassure the committee that we don't take this lightly at all, every effort is made to find people who are not answering their phones to come for testing.
"In Covid-19 tracing hubs, at least four or five attempts are made to contact people. Where there is an inability to find them, their details are sent to the public health department as they might have local knowledge about how to find the contacts."
A Garda spokesman said it does not comment on remarks by third parties and that the public health regulations are a matter for the Department of the Health.
Second wave
The committee also heard that the health service is better prepared to deal with a second wave of coronavirus if one happens.
Dr Kevin Kelleher, HSE assistant national director of public health and child health said: "I think we have learned a lot, we have got better prepared , we have got better resources available to us in terms of the knowledge we have learned as an organisation and we have got staff who now know what we need to do and we have got PPE in place."
Dr Liam Woods, HSE national director of acute hospitals said there is more guidance and training available to HSE healthcare staff but challenges will remain.
"The challenge is one that has been flagged to the committee and that is one of addressing the challenge of winter and the challenge of Covid-19 on top of winter."
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