The Health Service Executive (HSE) says people tested for COVID-19 should get a result within 48 hours by the middle of this month.
It is aiming to ramp up testing to 100,000 a week from May 18th.
There has been criticism after some people had to wait weeks for a test result in the past.
HSE CEO Paul Reid says they are aiming to improve that.
"During May, and indeed on the 18th of May, that we maximise that now to about 48 hours from the time the swab test was taken to the delivery of the result.
"And about maximum three days overall from the time a person contacts us to the time of their result - that's the plan".
Mr Reid also said there were "positive trends" showing, after a further fall in the number of people being treated with COVID-19 in Intensive Care Units (ICU).
The latest figure is 98 - only the second time it has been less than 100 in the last month.
On Friday, that figure stood at 99. This is from a high of 160 back in April.
Dublin's Mater, St James's and Tallaght Hospitals have the highest number of confirmed cases.
However he added that it was still "far too early" to make judgement about these figures.
