The Health Service Executive has issued a statement saying that GP out of hours services, HSELive and emergency numbers 112 and 999 have been receiving a very high number of calls from people seeking access to testing for Covid-19.
The HSE said it was working to have "new electronic processes" in operation from Monday to deal with the increased demand in testing.
It said: "While GPs have had access for some time to testing through the National Ambulance Service, given the increased requirement for testing, 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".
It said 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 needed.
The HSE said it is working this weekend to ensure that sufficient testing facilities are in place by then to meet the demand.
"GPs out of hours services are not in a position to order testing for patients with normal cold and flu like symptoms."
The HSE's information line is also similarly not in a position to order testing for members of the public, it said.
The public are being asked to only use 112 or 999 for medical emergencies at all times.
"While we appreciate people's concern about Covid-19, we would ask for their patience as we respond to the increasing requirement for testing," said Dr Colm Henry, Chief Clinical Officer of the HSE.
The announcement comes as the body representing GPs said they are "very concerned" that they will be swamped with calls on Monday morning after the Department of Health lowered the threshold for testing of Covid-19.
The President of the Irish College of GPs Dr Mary Favier said that GPs will be "exceptionally busy" from Monday and it may take time for them to return calls to patients in the wake of the changes.
She said out of hours services are under huge pressure this weekend and she appealed to people not to contact them unless they are unwell.
Dr Favier said if people have symptoms of Covid-19 they should socially isolate and that on Monday GPs could arrange an appointment for testing.
She also reminded people not to attend their GPs in person if they have symptoms of Covid-19.
Around 80% of cases of Covid-19 will be a mild to moderate illness, close to 14% have severe disease and around 6% are critical.
Generally, you need to be 15 minutes or more in the vicinity of an infected person, within 1-2 metres, to be considered at-risk or a close contact.