Some people testing positive for coronavirus have had up to 50 contacts, according to the head of the HSE.
Paul Reid has admitted the COVID-19 testing and tracing systems came under "immediate strain" due to the increased numbers of cases.
However, he has dismissed any claims that the system is falling apart.
It now takes a median time of 2.3 days for a person to get a referral for a test, get informed of their result and for their contacts to be identified.
Earlier this week, Trinity College Immunology Professor Tomás Ryan said the system was not fast enough and that he believed it was falling apart.
Mr Reid today insisted that they are meeting the current testing demand.
He said: "Such alarmist comments - which is what they are - may get attention, but they are not borne out by the facts.
"In my view, they are hugely unhelpful.
"We want people to come forward for testing, and demonstrate that the testing system is meeting demand - which is what it did last week."
Mr Reid acknowledged that the spike has caused "immediate strain" in terms of turnaround time, but there are strong processes in place to allow for an increase in testing capacity.
He also said that a total of 55,000 tests were completed in the last week - representing the second highest figure since the outbreak began here almost six months ago.
In terms of contact tracing, Mr Reid said: "The increased contacts per person... sometimes the mean or average doesn't always get the full picture... but in some cases [there have been] well over 40, even up to 50 contacts per person."
