Public Health Wales (PHW) officials were responding to Welsh Government plans launched in November.
PHW backed moves to restrict smoking but said ministers should go further.
The body was giving evidence to the assembly's health committee.
The proposals are part of the Welsh Government's second attempt to bring in the Public Health Bill, that does not include a controversial ban on e-cigarettes in some enclosed places.
Ministers hope the legislation will be passed by May.
PHW's submission to the committee said: "We would suggest that there would need to be a clear definition of 'playground' and that 'schools' should include early years educational settings such as nurseries (private and public).
"In the case of schools and playgrounds this should include the perimeter of these settings otherwise the intended impact of the restrictions is unlikely to be achieved i.e. if parents or other adults are permitted to smoke at the perimeter of a playground or at the school gates in clear view of children this will not impact on the intended goal of 'denormalisation' (reduce smoking being modelled to children as normal behaviour).
"We would also propose that the restrictions should not be limited to hospitals but should include the grounds of premises used predominately for the delivery of healthcare to include community health facilities and primary care."
Currently, the Welsh Government plans to ban smoking within five meters of playground equipment "due to this being beyond the distance of potential second hand smoke harm from a single cigarette, plus an additional buffer to protect against weather elements".
On Wednesday, PHW Director of Health Improvement Dr Julie Bishop told the committee that a broader definition of a "playground" was needed.
"If we're narrowing that definition to, literally be play equipment; so I presume by that we mean things like slides and swings and those kind of things, that's actually quite a small area of what most of us would consider to be playgrounds in the broader sense," she said.
"So I would encourage playing fields and sports grounds to be included in that definition."
Plans to ban smoking in school and hospital grounds and playgrounds in Wales should also extend to outside all nurseries, GP practices, playing fields and sports grounds, a health promotion body has told AMs.