The new Covid-19 tracker app will be able to alert people who were close contacts of a person who tested positive for the virus within hours, as opposed to the days it currently takes in some cases, HSE chief Paul Reid said.
Contact tracing is seen as a key part of the health service's ability to respond to new outbreaks following the easing of restrictions.
As of 9pm yesterday, the free app had been downloaded 730,000 times.
Mr Reid said 43,000 people were tested last week.
The average time from when a person gets a referral for a test to when their contacts have been traced is now running at less than two days.
The target was to complete this process within three days in 90pc of cases.
"The app fits in as part of that process. It is not a silver bullet but a significant element in contact and tracing," Mr Reid said.
Health Minister Stephen Donnelly appealed to people to download the app.
It involves four separate strands - automated contact tracing, symptom tracking, daily information updates and the submission of anonymised data on user behaviours to the HSE.
"Together we have made a huge collective effort in recent months to limit the spread of Covid-19," Mr Donnelly said.
"As we ease restrictions, many important aspects of Irish life are returning and we are able to access more services and to meet more people.
"The introduction of the Covid tracker app will allow us to speed up reporting and tracing from the first onset of the symptoms of Covid-19, making the app's role in testing and contact tracing vital to the continued momentum of the reopening of Irish society and business."
He said that if every one of us asked everybody in our network to download, "we would be where we need to be".
The app, which is available from the Apple and Android app stores, works at its core by using Bluetooth technology to exchange 'handshakes' between different users.
There are anonymous keys to alert a user to being a close contact of someone who has tested positive.
A close contact is someone who was within two metres of a person who has tested positive for 15 minutes or more.
The close contact will be asked if they want to undergo a test for the virus.
Health officials are hoping for a 60pc uptake of the app, but any uptake would help.
Acting Chief Medical Officer Dr Ronan Glynn said people are being asked to download the app and "until we have a vaccine or an effective treatment, testing and contact tracing are vital to our ongoing collective efforts to minimise the spread of Covid-19".
He added: "The app is integral to contact tracing, working in tandem with the key public health measures of social-distancing, hand washing, covering our coughs and wearing face coverings, helping us to stay safe and to protect each other."
One of the hurdles faced may be persuading people to go for a test if they are found to be a close contact. Between mid-May and the end of last month, 35pc of those identified as a close contact of a confirmed case did not take up the offer of a test.
Dr Glynn said every case has the potential to turn into a cluster, which in turn has the potential to spread through a community.
"If you are identified as a close contact, please take up the offer of a test without delay," he added.
Commenting on the 730,000 downloads, he said it is one more example of the solidarity and collective spirit that has characterised the Irish public's response to Covid-19 to date.
"The app has the potential to reduce the time people are active in the community with infection, which will have a significant impact on the transmission of the disease," he said.
"The more people who download and use this app, the more effective it will be.
"It is a further opportunity for us to play our part in the response to Covid-19."