Waterford recorded less than 10 new cases of Covid-19 over the last 15 weeks, while Kerry had less than 10 cases for 14 consecutive weeks.
There were also fewer than ten cases recorded over the previous 13 weeks in Leitrim, Longford and Tipperary, according to the Central Statistics Office (CSO).
A local lockdown was imposed on Kildare, Laois and Offaly last week. Those three counties accounted for two-thirds of all new cases for the week ending August 7.
The CSO’s latest Covid-19 bulletin shows that females and those aged between 25 and 44 still make up the highest number of cases.
However, the number of people who have died from the virus has been below 10 for the last six weeks and no deaths were recorded for the week ending August 7.
Dublin continues to be worst hit with 51% of the total confirmed Covid-19 deaths, and there were 58 new cases diagnosed last week.
The weekly number of confirmed Covid-19 cases nationally is over 100 for each of the past five weeks.
There were 509 confirmed Covid-19 cases in the week ending August 7, an increase of 224 on the previous week.
Over half (54%) of confirmed cases are linked to an outbreak and almost half (46%) of new cases are linked to an outbreak in the workplace.
It was the fifth week in a row that there was a rise in cases linked to outbreaks in private homes.
The virus has accounted for the deaths of 1,519 people, and a further 253 deaths are cited as probable deaths due to the virus.
Chronic heart disease was present in 44% of deaths and of the 112 deaths in the 25 to 64 age group, 104 had underlying conditions.
Older age groups remain the hardest hit by Covid-19, with 64% of people who died aged 80 or older.
The overall mortality rate is 57 per 1,000 confirmed cases and was highest in April at 73 per 1,000 but fell to a consistent level of 38 and 34 in May and June.
Last week, eight people were hospitalised, down from 648 at the peak at the end of March.
For the 11th week in a row, there have been less than five people admitted to an intensive care unit, with the admission rate at 17 per 1,000 cases, compared to 27 per 1,000 in March.