The plan to restrict the promotion of foods high in fat, salt and sugar to under 16s is being consulted on by the Committee of Advertising Practice.
It would see the existing ban on TV ads extended to all media, including online outlets, the industry regulator said.
Current limits on using celebrities and characters to sell food to children could be relaxed for healthier foods.
About one in five children in the England is classed as obese by the end of primary school, according to the Health and Social Care Information Centre.
The self-regulatory body, CAP, which sets rules for UK advertising, said the new rules could make a "meaningful contribution to tackling this important health issue".
Currently, food and drink deemed unhealthy can be advertised to children in non-broadcast media, unlike television where strict regulation prohibits it through content and scheduling restrictions.
Ofcom research suggests that 96% of 12 to 15-year-olds spent more time online than watching TV last year.
The advertising industry needed to make sure its regulations reflected changing media habits among young people, CAP said.
Evidence showed advertising had a "modest" effect on children's food preferences, it said.
However, factors such as parental influence, opportunities for physical exercise and education playing a greater role in solutions to childhood obesity, it argued.
Chairman James Best said: "Advertising is just one small factor in a very complex equation but we believe we can play a positive part in addressing an urgent societal challenge.
"In proposing new rules, our aim is to strike the right balance between protecting children and enabling businesses to continue advertising their products responsibly."
Alex Neill, of consumer watchdog Which?, said a rule change was "long overdue", and vital to tackling childhood obesity.
But Children's Food Campaign co-ordinator Malcolm Clark said the proposals had "too many gaps in the detail of the consultation and scope for the rules to be weakened".
The regulator had "missed obvious opportunities to make the UK a world leader in putting the protection of children's health above food and advertising industry profits," he said.
The consultation closes on 22 July.
A complete ban on advertising unhealthy foods to children is being considered as a way to reduce childhood obesity.