The Chief Medical Officer has appealed to people to adhere to travel restrictions and to stay at home.
Dr Tony Holohan's call came amid concerns that some holiday home owners are travelling to other parts of the country ahead of the Easter weekend.
Gardaí conducting regular road checks around Conamara (Connemara) say they have noticed an increase in the numbers travelling longer journeys.
Local representatives there have appealed to people to adhere to the guidelines in place regarding self-isolation and social distancing.
Fianna Fáil Councillor Gerry King said the area was renowned for the welcome it extended to visitors but it was now time for people to follow public health advice and work to slow the spread of Covid-19.
Those sentiments were echoed by Terence O’Toole, of the Connemara & Aran Islands Tourism Network.
He said he hoped the sector would begin to see a return to some kind of normality in the coming weeks.
For now, Mr O’Toole said people should "hang back" and avoid holidays until restrictions on travel were lifted.