The Irish Nurses and Midwives Organisation (INMO) has asked the Health Service Executive (HSE) to re-examine all its infection and prevention controls for staff.
It comes as close contacts of coronavirus patients are being asked to return to work in the health system, provided they have no symptoms.
The HSE has said close contacts are being called back in due to the risk to patient safety posed by staff shortages.
It said the staff will undergo additional monitoring twice a day and will be prioritised for testing.
But Phil Ni Sheaghdha, general-secretary of the INMO, told The Hard Shoulder more needs to be done.
"The big issue here is that we do not have a routine testing and tracing system in the acute hospital service.
"We do, and we have had that system in place, in long-term care for some time.
"But in order to ensure that somebody is not a risk, you have to make sure that you know that: the only way you know that is by routinely testing".
She explained the only testing in the acute hospital sector is, in the event of an outbreak, those who are deemed close contacts.
She added that routine testing is important "to pick up asymptomatic cases".
"We're now looking at 2,500 positive cases in healthcare workers a week, and the HSE advised that 50% of those are patient-facing staff".
"We're calling for a re-look at all the protections that are in place - part of that is screening, and part of that is routine testing".
"We have notified and asked the HSE today to re-look at all of the infection and prevention controls they have in place for staff - because clearly, something is not working if the rate of infection is this high".
This would also include examining the use of higher-grade PPE in certain settings, she said.
She said they should also be 'looking at' what supports the private hospitals can bring.
Ms Ni Sheaghdha added that the INMO's policy on this has not changed.
"This is a policy that has been in existence in the HSE, and was used in the first wave.
"We found at that time that the incidences of healthcare workers actually increased as a result.
"Certainly we're not in favour of it - we've [sic] made our position clear and known to the HSE at that time and our position hasn't changed".
"We know more about this virus, and we know that asymptomatic does not mean you're COVID free or that you're not a risk of passing the virus on".
"So it makes no sense to us...that you have somebody who's asymptomatic coming back - even if you test negative, remember.
"You can test negative today but if you're a close contact you can be positive tomorrow."
"What we would prefer to see is that we really focus on supporting the healthcare workforce by ensuring we have childcare available - so that those that can come to work are able to come to work".