The Minister for Health, Stephen Donnelly, said he strongly refutes claims by Sinn Féin that the testing and tracing system has "collapsed".
He said 117,000 tests have been carried out in the past seven days, which he said is one of the highest rates in the world.
He added that contact tracing has been scaled up by 400% in a period of six weeks.
In mid-September the HSE had 231 staff working on contact tracing, in four week's time they will have 800, he told the Dáil.
"Right now they have assured me they can deal with 1,500 positive cases a day and do full contact traces," he said.
"If you honestly believe that the testing and tracing system has collapsed, that is fair enough. But I would strongly refute that," he added.
The Minister told the Dáil: "We've got to stop this pile on every time they [HSE] make a mistake. They are going to make mistakes, I am, and Government is as well, we are dealing with a national pandemic, this is not business as usual."
His comments comes as the head of the National Virus Reference Laboratory has said the staff shortages at the NVRL this weekend and next will "have no impact" on the capacity for testing.
Speaking on RTÉ's News at One, Dr Cillian De Gascun explained that one of the two teams of testers is self-isolating after one of its members tested positive for Covid-19 earlier this week, and the second team has been in place for the remainder of the week.
He explained that it was agreed with the HSE that the team would be "allowed time to recover" this weekend and next, as there are less demands on testing during this time.
Dr De Gascun said he was surprised that this issue has "captured so much attention."
He said: "It will have no impact on the testing capacity over the course of the relevant timeframe. There is plenty of spare capacity at the weekend to pick up the slack"
Dr De Gascun said: "It is not ideal but the HSE has put in a lot of work to ensure that there is sufficient on-island capacity to perform the testing."
He said this is the first time that testing teams have been affected by Covid-19, and since the staff were split into two teams in March.
Speaking on the same programme, the co-leader of the Social Democrats Róisín Shortall said that the reduced availability of the laboratory is a warning sign that staff working in testing and tracing are overstretched and an emergency plan for contingency staff needs to be put in place.
Ms Shortall said that given the testing and tracing system is the bedrock of the Government's approach to tackling the virus, it cannot afford for there to be any more problems with it.
She said that unfortunately staff working in these facilities will succumb to Covid-19 and there is a need to identify other potential staff that can be brought in at short notice.
Ms Shortall said that she would be more assured to know there is an emergency plan that kicks in for testing and tracing.
In a statement, Labour leader Alan Kelly called on Minister for Health Stephen Donnelly to outline what contingency measures will be put in place to ensure that it does not "adversely impact and delay the processing of Covid-19 tests".
Mr Kelly said: "This is extremely concerning at a time when we are processing a record number of tests and case numbers are so high.
"Minister Donnelly needs to state how this will affect the processing of tests and outline what contingency measures will be put in place to ensure that all Covid tests are processed in a timely manner."