The Garda Representative Association (GRA) says the National Public Health Emergency Team (NPHET) must recognise their role in containing the spread of Covid-19.
The call comes as the Health service executive (HSE) ends priority testing for the Gardaí.
According to a GRA statement the HSE ended the arrangement with the Gardaí due to a "clinical governance issue."
The GRA said they were informed yesterday that arrangements for priority sampling were being abandoned.
Reacting to the decision, GRA President Jim Mulligan said: “We have been pressing this matter from an early stage of the crisis and were assured week after week that measures were being implemented.
“Sampling facilities had been organised in different parts of the country and we were told arrangements had been made with the HSE for speedy testing."
The President of the GRA said that NPHET had "scuppered" this plan and that the GRA learned of their decision after they had trained Garda members with medical experience to take samples.
Jim Mulligan said: "It is difficult to make sense of how there could be a governance issue around priority testing for Gardaí when there was none around other frontline workers such as medical staff and ambulance workers.
“We requested fast-tracking of testing gardaí as a Health & Safety measure for members because of their exposure to infection at work due to the huge volume of public interaction involved in policing at the moment.
“A fast-track testing procedure is needed to ensure the resilience of An Garda Síochána and prevent the potential danger infected gardaí could pose to the wider population."
Entire garda units are being forced to self-isolate because of the coronavirus, according to the Garda Representative Association.
The organisation is expressing its disappointment at the lack of priority Covid-19 testing for its members.
President Jim Mulligan says it is a disgrace that Gardaí have been told they will not be given priority testing.
He says: "Our members are very disappointed we have been looking for this since the very early stages of the crisis.
"We've had situations where one division a few weeks ago had 45 Gardaí go into self-isolation.
"We've had a unit in Dublin recently had to go into isolation awaiting a test result for a member who had contracted or been in close contact with [the virus]."
Gardaí have been told they will not be given priority Covid-19 testing, according to the Association of Garda Sergeants and Inspectors (AGSI).
The AGSI says it is deeply disappointed at the decision after management told the Policy Authority on April 20 that there would be priority testing.
The AGSI represents almost 2,500 mid-ranking gardaí and its general secretary, Antoinette Cunningham, says its members have been deliberately targeted during the Covid-19 crisis.
Ms Cunningham says: "We are the public face of making sure the virus does not spread, I think everyone would acknowledge that.
"Between April 8 and May 2, we have had 52 cases of people coughing or deliberately spitting on members of An Garda Síochána."
The general secretary said that priority testing would be "hugely helpful" to reducing stress levels among their members.
She says that it is "unacceptable" that members are not given priority testing.
Ms Cunningham says that members of An Garda Síochána members are being tested by their own GPs.