Patients who have not been given a time or date for their Covid-19 test will have to contact their GPs to see if they still meet the new requirements for testing.
GPs are also seeking a clarification on patients who have been given test dates but have not yet been tested in light of the new threshold.
The National Public Health Emergency Team (NPHET) recommended a change in requirements, bringing Ireland in line with the World Health Organisation (WHO) threshold for testing.
Patients now need to display two major symptoms, rather than one, before they will be referred for testing by their GP.
Patients will have to show a fever and at least one symptom of respiratory disease, such as cough or shortness of breath.
Previously, if a patient had either fever or cough, they could be referred but this led to a surge in demand and lengthy wait times for testing.
Anyone who has been swabbed to date will have their samples processed and tested.
However, the picture is less clear for those who were awaiting tests.
In a statement, the Irish Medical Organisation (IMO) and the Irish College of General Practitioners (ICGP) said they are "awaiting clarification" with regard to patients who have been given a test date but have not yet been tested.
Additionally, they said all patients who have not yet been swabbed and do not have an appointment for a test date will now not be tested.
"Such patients will be required to re-engage with their GP and the GP will triage the patient again in accordance with the new case definition," the IMO and ICGP said in a joint-statement.
"The Department and the HSE are of the view that in applying the WHO case definition and the prioritisation of criteria, this will allow for a focus on those in at risk population and those at the highest risk of exposure."
The new requirements are likely to lead a significant decline in the number of tests which, according to Chief Medical Officer Dr Tony Holohan, was unsustainable.
Almost 18,000 tests have been carried out to date. Just 6% of samples tested positive.
Over the weekend, it was reported that some 40,000 people were awaiting tests.
Dr Liam Glynn, Professor of General Practice at the University of Limerick, said he understands why the new criteria has been introduced but described the change as "regrettable".
Speaking on RTÉ's Today with Sean O'Rourke, he said, "Now we have lots of patients in General Practice who have been referred for testing and if they haven't received testing yet, will be told they have to go back to their GP and be re-triaged for testing.
"So you can imagine the anxiety that's going to cause among people who are waiting for tests,"
Dr Glynn said this will "significantly increase the burden" on general practices, who are already "flat out".