Updated at 20:15
The Chief medical officer, Dr Tony Holohan says there are "too many stories" of people with symptoms or waiting on tests not following instructions.
He expressed concerns as well about contacts failing to restrict their movements.
He also asked people to "Spread the word and make sure we all know what to do if we have contracted Covid-19 or if we have symptoms of Covid-19 or if we are awaiting a test result."
We need to have cases and contacts acting fully in accordance with advice.
There are too many stories of people with symptoms/waiting on tests and not self-isolating, also contacts not restricting movements.— Dr Tony Holohan (@DrTonyHolohan) October 26, 2020
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It comes as three further deaths and an additional 939 new cases of Covid-19 have been confirmed this evening by the Department of Health.
It brings the total number of Covid-19 related deaths in Ireland to 1,885.
There is also now a total of 58,067 confirmed cases of Covid-19 in Ireland, with tonight's figures.
The Department of Health said that of the cases notified today: 444 are men while 483 are women, 66 per cent are under 45 years of age and the median age is 32 years old.
262 of today's cases are in Dublin, while there are 96 in Cork, 61 in Meath, 53 in Galway, 51 in Donegal and the remaining 413 cases are spread across all remaining counties.
There are currently 344 people in hospital with Covid-19 and a further 37 people with the virus in ICU.
It comes as yesterday 1,025 new cases of Covid-19 were recorded in the Republic.
The Department of Health also revealed that the country's 14 day incidence rate per 100,000 is now 309.9.
There have also been a total of 14,758 new cases of the virus from October 12th up until midnight on October 25th.
