Almost 3,000 coronavirus tests are now being carried out every day, according to the director of the National Virus Reference Laboratory.
Dr Cillian De Gascun says he is confident testing capacity won’t be a barrier to lifting some restrictions next month.
He also said the main goal is to get to where we can 'test as much as we need to test' - and that we're now very close to that point.
There are now almost 11,500 coronavirus cases here, while 406 people have died.
A number of concerns have been raised about testing issues that have arisen in recent weeks.
On Monday the HSE confirmed there was a backlog of around 11,000 tests - with CEO Paul Reid saying they hoped to have that backlog cleared by the end of this week.
Meanwhile, some people have reported wait times of two weeks or more for the results of their coronavirus tests.
The issues come amid the global shortage of the reagents needed during the testing and analysis process.
Dr De Gascun - who is Chairman of the Coronavirus Expert Advisory Group - told Newstalk Breakfast that testing levels here are improving.
He said: "There has to be a small caveat that there is a global pandemic, and there will still be pressures and supply chain issues.
"But I think we have enough diversity and robustness in the system - and contingency as well - that by the time May 5th we certainly won't be in a position where the testing and contact tracing prevents us from being able to lift restrictions."
Confirming that testing is now in the 'high two thousands... approaching three thousand', he said a number of recent developments have allowed labs here to increase the testing capacity.
He observed: "It's been a good week from a testing capacity standpoint.
"With our colleagues in Germany... they've in essence cleared all the samples that had been waiting for two weeks... or in some cases two and a half, three weeks.
"We're in a much better position than we were this day last week."
