According to reports in the Times and Telegraph, calorie limits of 928 for pizzas and 695 for savoury pies could be introduced under new draft proposals.
Fast food restaurants, coffee shops and pubs were all represented.
Dr Alison Tedstone, chief nutritionist at PHE, said: "These are early days in the calorie reduction programme, but the food industry have a responsibility to act.
"The simple truth is on average we need to eat less.
"Children and adults routinely eat too many calories and it's why we've seen severe obesity in 10 to 11-year-olds at an all-time high."
She added: "We hope to see early commitment from the food industry – including the people who make, sell and deliver our food – translated into real action, sooner rather than later."
In England, a third of children leave primary school overweight or obese – with some children consuming 500 more calories per day than is recommended.
Duncan Selbie, PHE's chief executive, said excess calorie consumption is the food industry's "next big challenge".
In a statement released after the meeting, he added: "This is the promising start we need to succeed in reducing calories in the foods included in the programme by 20 per cent."
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