The chair of the Coronavirus Expert Advisory Group says 15,000 tests a day will be able to be carried out by the end of next week.
Dr Cillian de Gascun says people should also face less of a wait to get their test results.
"It'll be within 24/36 hours - that's what we're aspiring towards.
"And to be fair, that will happen because the structures are now in place to allow that to happen".
Meanwhile the country's main COVID-19 testing laboratory has only been able to operate at 40% capacity over the last two weeks.
Dr De Gascun, who is also director of the National Virus Reference Laboratory (NVRL), says this is because of problems sourcing enough of the chemicals that are needed.
"The NVRL has only been able to operate at around between 30 and 40% capacity for the last two weeks.
"That's really sort of the impact that this had had on the testing capacity that we thought we would have, almost as a banker.
"I certainly didn't foresee the fact that we would be so curtailed by global supply chain issues".
He says a quick turnaround is still a few weeks away.
"When we match the number of people coming through the sampling hubs with the laboratory capacity, then we would envisage people calling their GPs, they'll be referred - say for example if we start on a Monday - they call their GP on a Monday, they get an electronic referral, they will ideally be sampled in one of the community hubs on Tuesday, that sample will come to the lab - and the results will be available on the Wednesday or the Thursday".
It comes after Health Minister Simon Harris said the backlog of tests shipped to a German lab for analysis should be completed by the end of next week.
He said between 25,000 and 30,000 were sent and 14,000 have been returned.
It was confirmed on Friday just over 1,000 of those are COVID-19 positive.
Minister Harris said the remaining tests left to be completed will be done over the coming days.
"It is our hope, our expectation and our plan that by the end of next week, any backlog in relation to testing will have been addressed.
"And we want to move to a place where people can get their test results within 48 hours.
"So we built up the capacity here in Ireland to ensure that that's in place in terms of lab capacity, swabs and testing centres.
"And we're dealing with the legacy backlog, if you like - and that will be dealt with by next week".