Only around half of doctors around the country have signed up to provide free GP care for children under the age of 6.
The HSE has released figures on the number of doctors who have signed contracts for the scheme, which is due to be rolled out from July.
The lowest uptake is in South Tipperary with only 8% of doctors signing up to the scheme.
There has also been a low uptake in Cork - North and South - Kildare/West Wicklow, Limerick, Louth, Meath and Wicklow.
Donegal, Roscommon and Longford/Westmeath have seen the highest levels of uptake.
Many GPs have expressed concern about their ability to take part in the scheme - saying they do not have the resources to deal with the anticipated increase in workload.
Dr Yvonne Williams, who is based in Shannon in Co Clare and is a member of the National Association of General Practitioners, said it could make the overall health system worse.
"We do know that even in counties where they do have high numbers that have signed, GPs are doing it under duress," she said.
"I have not met a single GP who believes that this contract is in the best interests of patients since this contract has been published.
"They are concerned for their patients' safety and they don't want to see what has happened in the [British] NHS happen in Irish general practice.
"At the moment, most people are able to see their GP within a day or two of becoming unwell, in the UK that can stretch up to two weeks, and it's the same in Northern Ireland."
Carlow/Kilkenny - 50 - 71 - 70%
Cavan/Monaghan - 32 - 67 - 48%
Clare 36 - 53 - 68%
Cork – North Lee - 34 - 117 - 29%
Cork – South Lee - 30 - 134 - 22%
Donegal - 83 - 89 - 93%
Dublin – North Central - 46 - 78 - 59%
Dublin – South City - 49 - 93 - 53%
Dublin – South East - 17 - 53 - 32%
Dublin – South West - 42 - 76 - 55%
Dublin – West - 30 - 42 - 71%
Dun - Laoghaire - 24 - 74 - 32%
Galway - 130 - 169 - 77%
Kerry - 36 - 87 - 41%
Kildare/West Wicklow - 20 - 80 - 25%
Laois/Offaly - 38 - 68 - 56%
Limerick - 31 - 110 - 28%
Longford/Westmeath - 56 - 69 - 81%
Louth - 15 - 68 - 22%
Mayo - 63 - 85 - 74%
Meath - 19 - 68 - 28%
North Cork - 39 - 55 - 71%
North Dublin - 58 - 124 - 47%
North Tipp/East Limerick - 18 - 39 - 46%
North-West Dublin - 45 - 62 - 73%
Roscommon - 26 - 29 - 90%
Sligo/Leitrim - 46 - 58 - 79%
South Tipperary - 4 - 51 - 8%
Waterford - 43 - 68 - 63%
West Cork - 11 - 38 - 29%
Wexford - 41 - 68 - 60%
Wicklow - 20 - 70 - 29%