Ten thousand children under the age of six were registered for free GP care during the first day of registration, according to the Health Service Executive.
The National Director of Primary Health Care at the HSE has said he was "extremely hopeful" that resistance by some GPs scheme will change.
John Hennessy said there were some parts of the country where the uptake by GPs was not as good as others, and he would prefer to have far more choice available to the public.
Speaking on RTÉ's Today with Sean O'Rourke, he said he hoped that in time more GPs would sign up and follow the majority of their colleagues, as the only ones losing out are parents and children.
Registration for the scheme, which will be available from 1 July, opened today.
The HSE recommends that parents and guardians who wish to register children under-six go directly to the registration system page as the website gpvisitcard.ie is receiving huge volumes of traffic and has crashed several times.
Following the website crash, the HSE has assured people there is plenty of time to register.
A list of GPs who have signed up to provide free care is available on the website.
This evening, the number of GPs that have taken up the contract is just under 1,500, with considerable variation in figures across the country.
Minister for Health Leo Varadkar has said he is absolutely certain more GPs will sign up over the coming two weeks.
He told RTÉ's Six One News it is a matter of choice for GPs whether to sign the contract or not, adding it was a big change, which can sometimes create anxiety among health professionals.
Mr Varadkar said parents can choose another GP, should their current doctor decide not to sign up to the scheme.
The Minister urged parents to register their children and to be patient over the next week or two, during the scheme's transition phase.
Figures available at the weekend indicate a wide variation in take-up among doctors - the highest rate was in Donegal where 94% had registered.
The latest GP support stats for the u6s free GP care scheme... pic.twitter.com/TmwLlO6ipR
— Fergal Bowers (@FergalBowers) June 15, 2015The lowest was South Tipperary where just 8% had agreed to the new contract.
If parents cannot find their local GP on this list they are advised to contact the GP practice directly.
Opposition accuses Government of 'vote buying tactics'
Fianna Fáil has accused the Government of rolling out the scheme for free GP care for the under-sixes, in a ham-fisted way.
Party spokesperson for heath, Billy Kelleher, said Government members had committed to giving free GP care to everyone by the end of their term in office but were now panicking and rolling out the under-sixes scheme as an electoral "vote buying process."
Speaking on RTÉ’s News at One Mr Kelleher said Fianna Fáil was not criticising the scheme, just the implementation of it.
"We've large parts of the country where effectively very few GPs have signed the under-sixes contract" he said.
He accused Minister for Health Leo Varadkar of wanting parents to "traipse around the country trying to find a GP that actually has signed up to the under-sixes contract and that simply is unacceptable."
Minister of State with responsibility for primary care Kathleen Lynch has said the Government is working on how to provide free GP care for the under-sixes in parts of the country where very few doctors have signed up to the scheme.
Speaking on RTÉ’s Morning Ireland, Ms Lynch said the Government had anticipated that there would not be complete cover for the entire country and has been working on what will be done when parents cannot access a GP within a reasonable distance.
The minister said the new scheme may mean parents will go to their GPs earlier but this did not mean they would make unnecessary visits.
The Government says free GP care for under-sixes is the first stage in the roll-out of universal free GP care.
Over 70s will be covered from early August.
