The Health Service Executive has promised to speed up the turnaround time for Covid-19 test results and for contact tracing.
Over 250,000 tests have now been performed and the number of patients testing positive is reducing.
The HSE said it has the capacity to meet the demands for Covid-19 testing, even with the recently expanded test criteria.
But it said that some of the delays in results and contact tracing are because a complex new system had to be built in around eight weeks.
Over a quarter of a million tests have now been performed and the positivity rate is down to 3.3%.
The HSE said that test delays are not due to any single cause but can be down to a lack of automation, transcription errors, and hospitals having different computer systems.
It said some contract tracing is complex, especially in long term care facilities, where vulnerable patients may have communication difficulties.
HSE Clinical Lead Dr Colm Henry said the entire process can take around five days or more and the HSE wants to reduce this to three days.
Yesterday, the Department of Health said a further 24 people with Covid-19 have died, bringing the overall death toll to 1,488.
An additional 107 more cases of the coronavirus have also been diagnosed, bringing the number of confirmed cases to 23,242.
The chair of the new Dáil committee on Covid-19 said he would like the group to work through consensus and will focus initially on the capacity of the testing and contact tracing regime.
Speaking on RTÉ's Morning Ireland, Michael McNamara said Chief Medical Officer Dr Tony Holohan, HSE CEO Paul Reid and Secretary General of the Department of Health Jim Breslin will be the first witnesses before the committee.
Mr McNamara said the committee will look at the targets set for testing, adding the public have been given lots of targets but anecdotally it appeared these targets are not being met.
He said some civil servants had been trained to help with contact tracing, others were not and this issue also merited examination.
He said the committee would also urgently look at what is happening in care homes, nursing homes and in direct provision centres and look at the opening up of the construction sector, which is due to begin next week.
The 19-member committee held three-and-a-half hours of private discussions yesterday.
Mr McNamara said this first meeting was taken up with largely technical issues about how it would operate, how to allocate speaking time and about putting a work programme in place, adding that the committee has "divergent views and different parties represented" and he hopes it would work through consensus.
Meanwhile, a smartphone "opt-in" Covid-19 contact-tracing app is expected to be rolled out shortly.
It is being developed by the HSE, which is in discussions with the Data Protection Commissioner in relation to privacy issues.
The Bluetooth-enabled app is one way of alerting individuals that they may have been exposed to the virus, even by a stranger.
HSE Consultant in Public Health Medicine Dr Sarah Doyle told RTÉ's Prime Time that every aspect of the app's development is being closely scrutinised and monitored.
The School of Computer Science and Statistics at Trinity College Dublin has carried out a study into the reliability of the Bluetooth technology used by the contact tracing app.
Around 2,000 people will be involved in the initial deployment of the app in early June, before it is made more widely available.
Around 80% of cases of Covid-19 will be a mild to moderate illness, close to 14% have severe disease and around 6% are critical.
Generally, you need to be 15 minutes or more in the vicinity of an infected person and within 2 metres of them, to be considered at-risk, or a close contact.
