Dr Nikki Turner, the Child Poverty Action Group's health spokeswoman, also welcomed the new policy.
"It's really important for families. It takes the pressure off them about the cost of visiting their GP.
"It's important for the people who have to sit at home and wonder whether they should take their sick kids to the doctor or not.
"It's got to be part of a bigger picture that includes housing, includes decent incomes, but it's one component and it's really important."
General Practitioner Council chairwoman Dr Kate Baddock said free under-13s care was a great move, but her group would have preferred targeting of the extra funding towards healthcare for the families in need, rather than being universal.
GPs would need to read the policy's details before signing up, to ensure the funding available if they agreed to take part was sufficient to keep their practices sustainable.
The Pharmacy Guild said the policy was "a big win for communities".
"It will be of significant help to families struggling to cover medical costs and pay co-payments for their children's medicines," said chief executive Lee Hohaia.
Health Minister Tony Ryall said more than 400,000 primary-school-aged children were expected to benefit from the investment.
He said the existing free-under-6s scheme, under which GPs get top-up funding if they agree not to charge fees for infants, had led to reduced hospital admissions of children under 5 with conditions that were readily treated in primary care.
When asked if he thought free-under-13s was a good election policy, he said, "It's good for families and children; that's what we are principally interested in."
Opposition parties have previously promoted increased state funding to reduce fees for school children.
The Budget increases Vote Health by about 6 per cent, to $15.6 billion. Other new spending, spread over four years, includes healthier eating and exercise ($40 million), cancer treatment ($32.7 million), and elective surgery ($110 million).
Road to recovery
• Free care for under-13s
• No charge for medical visits to GP
• Includes after-hours visits
• Optional for GPs to sign up for the scheme.
• Starts in July next year