The HSE is promising a three-day turnaround for coronavirus tests from next week.
HSE chief Paul Reid said it has the capacity to carry out 15,000 tests a day as the country enters the first phase of the exit from lockdown.
People who get a negative result will be told in two days or less, he said. For those who test positive it will take three days to begin tracing their contacts who might have been exposed to the virus.
It comes as a further 10 deaths from coronavirus were announced yesterday, bringing the death toll to 1,506.
A further 426 cases have also been confirmed, bringing the total number of confirmed cases to 23,827.
Testing has been beset by delays but it is crucial to have a fast system in place as lockdown eases in order to pick up any increase in infection.
Mr Reid said only 3pc of cases were positive, so out of 12,000 cases 450 people would have the virus.
Most of those are straightforward when tracing their contacts but there are complex cases, such as people who don't speak English, nursing home residents or patients in intensive care.
The system is currently hampered by blockages including reliance on manual processes and the problem of some computers not talking to each other.
Mr Reid said work is under way to increase automation.
"What we are dealing with is a whole history of legacy systems all across the country," he said, adding that there is a "range of separate systems that often do not talk to each other".
"The model we have put in place is there to scale up to whatever positivity levels rise within the community, so that's what we have to build for."
Politicians publicly setting targets which the HSE had found difficulty meeting is "not particularly unhelpful", Mr Reid added.
Meanwhile, it could take nearly two years to clear a backlog of postponed surgeries, including on cancer patients, which has built up in hospitals due to the coronavirus crisis, according to a major study published today.
The HSE study estimates a backlog of 16,419 surgeries has arisen over 12 weeks as hospitals ordered mass cancellations.
Researchers at the University of Birmingham estimate that over 28 million elective surgeries across the globe could be cancelled as a result of the Covid-19 pandemic.
The modelling study indicates that each additional week of disruption to hospital services will be associated with a further 2.4 million cancellations.
In Ireland, 15,396 surgeries and 1,024 cancer surgeries were postponed in 12 weeks.
In addition, 90 Caesarean sections were not carried out. If the obstetric surgeries are excluded it leaves a backlog of 16,419.
Research fellow Dr Dmitri Nepogodiev told the Herald that 139,000 operations are performed annually in Ireland, according to the European Health Information Gateway.
That amounts to 2,670 per week and it drops down to 1,787 elective non-obstetric operations once emergencies and elective obstetrics are excluded.
"If the backlog is 16,419, and we normally do 1,787 operations pre-pandemic, and increase that by 10pc we would be clearing 179 operations from the backlog per week. So it would take 92 we eks to clear," he said.
This could be reduced to 46 weeks if it was increased by 20pc, and cut to 31 weeks if another 30pc of surgeries were carried out.
The HSE has said it will use private hospitals to help to clear the backlog but the additional restrictions on physical distancing will slow things down.