HSE Paul Reid says it's essential for all close contacts of confirmed COVID-19 cases to come forward for a test.
There were more than 14,000 no shows at coronavirus test centres last month, figures from today's Business Post show.
Mr Reid says 94% of close contacts now come forward for a test, but those who don't are putting others at risk.
He explained: "We make contact with people once they're identified as a close contact - and we schedule their appointment for a test, and it's really important they do come forward.
"If they don't come forward for a test, we do make contact again and reschedule for them."
While the current average positivity rate for testing is less than 4%, that rises to 12% for close contacts.
Mr Reid said he understands people are tired and wish the pandemic would go away.
He said: "Complacency sets in from a range of issues, whether it's public health measures or coming forward for testing.
"But the virus doesn't change, and we need to be consistent and relentless in our response to it."