People looking to be tested for Covid-19 have been flooding GP out-of-hours centres and the 999 emergency line today with a "high volume" of calls.
The HSE is asking people to keep 999 and 112 for emergencies only and says out-of-hours doctors cannot order tests.
The HSELive information line is also unable to order tests.
Members of the public who have normal cold and flu symptoms or who believe they may have been in contact with Covid-19 are being asked to self-isolate and call a GP on Monday.
The Irish College of General Practitioners (ICGP) has advised that from Monday GPs will be able to order the test electronically through their IT system, Healthlink.
GPs will not undertake the tests themselves to help protect their staff and other patients.
The ICGP said the HSE will have enhanced capacity for testing from Monday.
The HSE plan to have community COVID-19 testing centres established to enable testing at local level.
Officials say they are working through the weekend to make sure enough testing facilities are in place by Monday to meet increased demand.
"Individual GP practices will continue to look after their patients who have ongoing and acute illness, and we will continue to do so with the assistance of our dedicated staff,” said Dr Nuala O'Connor, the ICGP's Clinical Lead on Covid-19.
Dr Mary Favier, President of the ICGP said that patients who feel physically unwell and whose symptoms are worsening especially where there is shortness of breath or fever should contact their GP for advice during office hours or local Out-of-Hours service at evenings and weekends by phone.
They will be provided with advice over the phone about how to proceed.
“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.
Dr Henry said that he understands the concern and anxiety being felt by members of the public.
He added that the health service is working to provide the necessary information and to provide the testing and health care needed for those who due develop illness due to Covid-19.
Dr O'Connor is reminding the public that illness due to Covid-19 is generally mild especially for children and young adults.
"However, it can cause serious illness; about 1 in every 5 people who catch it may need supportive care," said Dr O'Connor.
"It is quite normal for people to worry about how the Covid-19 outbreak will affect them and their loved ones.”
The public are once again being urged to take steps to help to limit the spread of Covid-19.