Up to 1,000 people a day are not attending scheduled appointments for a community COVID-19 test.
The HSE is warning that this is becoming an issue at a number of its sites and is urging people who have been given an appointment to attend.
Labs processed 61,950 tests last week, with an average positivity rate of 1.3%.
HSE Chief Operations Officer Anne O'Connor said it is worrying that 25% of those offered a testing appointment are not showing up.
She said this is a particular problem when capacity will potentially be needed for schools.
She added: "There are some areas where this is more of an issue than others.
"We really need to communicate to people that because these appointments are automatically scheduled, and even though we can book people as much as possible, we are finding there are sites where people are not availing of their appointments and that means there's an appointment that somebody else could have used."
Earlier, the Chief Executive of the HSE Paul Reid said the mean end to end turnaround on testing, including the tracing contacts, was 2.2 days.
We recorded our highest completed #COVID19 tests at almost 62,000, last week. GP referrals up by 14%. The mean, end to end turnaround, incl. contact tracing was 2.2 days. Please ensure to give correct mobile contact details as this is a key factor in any delays.@HSELive
— Paul Reid (@paulreiddublin) September 3, 2020
He said the HSE is very pleased with how schools have responded to recent cases of COVID-19.
It comes after two schools in Kerry sent some of their students home today after pupils tested positive for COVID-19.
Over one million students returned to class over the past week or so, with cases of the virus also confirmed at two Dublin schools.
Additionally, a primary school in Co Clare closed after some staff members were deemed close contacts of a positive case.
