Almost 30,000 under sixes have now been registered for free GP care.
The HSE says there has been a steady stream of applications since the process opened on Monday.
From July 1, almost 300,000 children will be eligible to visit their doctor free of charge.
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The number of GPs registering is also climbing - with up to 100 signed up in the past few days.
Anne Marie Hoey is Assistant National Director of Primary Care Services with the HSE.
A full list of the GPs who have signed up for the scheme is available on the HSE website. Parents can also register their children online.