A group of 39 GPs in Tipperary said they will continue to refuse to join the scheme giving free visits to under-sixes from next month, writes Eilish O'Regan.
South Tipperary, along with west Cork and Dublin south-east, have a low take-up of GPs for the scheme.
The proportion of GPs who have signed up rose to 1,720 yesterday - 71pc of eligible doctors. It followed a decision by Dr Yvonne Williams, a Clare GP, to drop her High Court challenge backed by the National Association of General Practitioners (NAGP).
The NAGP described it as a dark day, but said it was a tactical withdrawal of the case. It is expected to open the way for many GPs who were awaiting its outcome to sign up to the scheme for which 36,000 children have already been registered.
South Tipperary GPs said they requested a meeting with Health Minister Leo Varadkar to discuss the contract "which fails to provide the necessary support and protection to ensure the continued accessibility, confidentiality and high quality expected by our patients".
A spokesman for the minister said no formal request was made.
"Given that Government policy is clear on medical cards for the under-sixes, it's not clear what purpose any such meeting would serve," he said.