Health Minister Leo Varadkar has told GPs who have still not signed up for the under-sixes scheme that the "train has left the station".
He insisted there was "no going back" and appealed to them to "get on board".
Mr Varadkar and Social Care Minister Kathleen Lynch formally launched the registration for the scheme at St Andrew's Resource Centre, in Pearse Street, Dublin yesterday, which houses a pre-school.
Both suggested the almost 40pc of GPs who are still holding out would sign up as they saw the volume of contracts coming in from their colleagues around the country.
GPs would also face pressure from their own patients who will ask them why they have not signed up, he added.
The minister ruled out any emergency meeting with the National Association of General Practitioners (NAGP) which is opposed to the scheme.
Asked what would happen if a particular GP practice had more under-six-year-olds registering than they could cope with, he said it was up to the doctor to decide what level of patients they could safely accommodate.
In general, they accept on a first come, first served basis.
Once the under-sixes get free visits it will be the turn of the over-70s in August.
The next phase would involve children under 12 and then teenagers under 18.
"No consideration" has been given to expanding it beyond those groups.
Ms Lynch said the extension of free GP care to the adult population will be a matter for after the next general election.
"This phase is about young families, out working with mortgages to pay," she said.
Ireland is behind other European countries in giving free access to GPs, they insisted.
Mr Varadkar said he had difficulty with assessing children's access to GPs based on their parents' income.
This is not applied when it comes to areas like education.
The number of discretionary cards has risen by 30,000 in the last year.