HSE Chief Executive Paul Reid has apologised to the 2,000 people who were told to alert their own close contacts after they tested positive for Covid-19.
Speaking on RTÉ's Today with Claire Byrne, Mr Reid said it was a "concerning" development for the HSE.
He said the executive has been recruiting 70 people per week for contact tracing and 220 people have been employed in tracing in the last couple of weeks, with a total of 500 people involved in testing and tracing.
He said: "The huge surge that emerged over the last ten days did catch us this weekend," and "our recruitment hasn't caught up with the rise in cases".
Mr Reid said they will get 70% of decisions right and 30% wrong, but that the most important thing is that decisions are made because if you wait for perfection, nothing will get done.
He said he stood over the operational decision made in relation to contact tracing and estimated that around four to five contacts per person (who tested positive last weekend and was subsequently asked to call their close contacts) were missed.
He said the HSE is continuously being transparent and his team were out yesterday explaining why these decisions were made.
Mr Reid said he takes full responsibility for not informing the Minister for Health about the situation.
He added that the story broke in the media as staff were trying to deal with the issue.
Mr Reid also said the decision over contact tracing at the weekend "was not a decision we took lightly", but one based on risk.
He said: "40% of resources that have to be recruited must be from allied health professionals.
"It is not a contact call centre. It is a clinical call that is the first call, and over the last number of weeks the nature of cases are increasingly complex and calls are taking "much longer".
Mr Reid said GPs have been asked to facilitate tests for the people affected by the move.
Chief Medical Officer Dr Tony Holohan told a press briefing this evening that problems with the contact tracing system are not the reason for the current rate of infection.
He said he was not being "too hard or too soft" on the contact tracing system. He said the evidence is that the risk is community transmission and the message is to follow public health advice.
As first reported by The Irish Times, the people involved were due to receive a text message, which could be forwarded with advice for anyone they deem to be a close contact.
In the message, the people who tested positive for the virus were to be asked to send on a message to their own close contacts - people they have spent more than 15 minutes with - alerting them to restrict their movements and to immediately contact their GP to arrange a test.
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Meanwhile, Fianna Fáil TD Jim O'Callaghan said that it is not tenable to allow the contact tracing system to become overwhelmed again and the state has an obligation to ensure there is an effective tracing regime into the future as otherwise it will undermine the Covid-19 testing system.
Also speaking to RTÉ's Today with Claire Byrne, he said it is a very difficult job for the HSE but that NPHET has been able to model the spread of the virus weeks ahead "so nobody should be surprised by the higher case numbers".
He said looking ahead we need to ensure we have adequate resources in place for contact tracing.
Earlier, Minister for Health Stephen Donnelly said it was incorrect to say that contact tracing had fallen down, adding that in the last six weeks contact tracing teams have made 400% more calls than previously.
Speaking on RTÉ's Morning Ireland, he said that for a short period last weekend there was a one-off situation where demand outstripped supply and a one-off operational decision was made to reset the system.
Mr Donnelly said he has no problem apologising to those who were asked to call their own close contacts but said it was important to remember this is the middle of a global pandemic and things are not operating as normal.
He defended the HSE testing and tracing system, saying the organisation has been "working night and day" and despite mistakes it has established one of the highest testing regimes in the world, backed up with a tracing app.
The Minister said the HSE has ramped up testing to 122,000 tests per day and he has been informed that contact tracing can now deal with 1,500 positive test cases per day.
Every single country is struggling to get testing and tracing functioning adequately, he added.
Test and trace cornerstone of virus efforts - ECDC
The testing and tracing regime is the cornerstone of efforts to control the spread of Covid-19 and it is vital that it is working well, an expert for emergency preparedness and response with the European Centre for Disease Prevention and Control has said.
Dr Agoritsa Baka also said the ECDC does not see the spread of the virus being driven by school settings, but that bigger clusters have broken out in workplace settings where there are indoor meetings and events such as in factories, mines and businesses.
Speaking on RTÉ's Morning Ireland, she said the second wave was expected and colleagues in the US are reporting that outbreaks among young people, which may have happened in the summer, did not lead to too many hospitalisations.
However, she said, they suggest that the virus then gradually spreads though the age ranges and progresses over 130 to 150 days to reach the elderly and more vulnerable groups.
Dr Baka said that between any surge people "want to go back to normal" and while it is really hard, they must maintain physical distancing.