The HSE is warning anyone with "normal cold and flu like symptoms to self-isolate" and to ring their GP on Monday.
The Health Service Executive has said that GP Out of Hours Services, HSELive and 112 and 999 have been receiving a high number of calls today from people who want to be tested for the deadly COVID-19 bug.
They are urging anyone with a normal cold and flu or who believe they may have been in contact with someone with coronavirus to act quickly.
In a statement, they said: "The HSE is working to have new electronic processes operational from Monday, March 16 next to allow General Practitioners more easily order testing for patients where clinically indicated.
"Members of the public who have normal cold and flu like symptoms or who believe they may have been in contact with COVID-19 are being asked to self-isolate and to ring their GP on Monday, who will then be in a position to triage patients appropriately and order a test where indicated.
"The HSE is working this weekend to ensure that sufficient testing facilities are in place by Monday to meet the increased demand.
"GPs Out of Hours services are not in a position to order testing for patients with normal cold and flu like symptoms.
"HSELive is an information line and similarly not in a position to order testing for members of the public.
"The public are asked to reserve 112/999 for medical emergencies at all times."
Dr Colm Henry, Chief Clinical Officer of the HSE added: "While we appreciate people’s concern about COVID-19, we would ask for their patience as we respond to the increasing requirement for testing.
I completely understand people feeling concern and anxiety.
We will all work together as a health service to provide the information you need, and to provide the testing and health care needed for those who do develop illness due to COVID-19.
The public should go to the HSE website in the first instance if they are concerned about COVID-19.”
On Friday, a further 20 cases of coronavirus were confirmed in the Republic of Ireland.
This brings the total number of cases on the island of Ireland to 119 - 90 in the Republic of Ireland and 29 in Northern Ireland.
