The government's food watchdog is pushing for a ban on TV commercials advertising junk food before the 9pm watershed.
The consultation will end on 30 June
The Food Standards Agency (FSA) says proposals drawn up by media regulator Ofcom to reduce the effect of junk food ads on children do not go far enough.
The three sets of options stop short of a pre-watershed ban.
But the FSA says banning such ads for products like crisps and fizzy drinks would help protect children's health.
It is estimated that 14% of children in England are clinically obese.
Earlier this year, Ofcom proposed tighter restrictions on the timing and content of junk food commercials as part of a consultation.
One option was to ban the ads in commercial breaks in programmes for pre-school children.
Another was to ban or restrict them in programmes for the under-10s.
At a meeting in Bristol on Thursday, the FSA rejected all Ofcom's options.
It argues a ban on junk food commercials before 9pm would extend protection to older age groups.
The British Heart Foundation (BHF) said it was "delighted" that the FSA was pressing Ofcom for a pre-watershed ban.
It claims more than two-thirds of parents would support such a move.
Campaigns officer Josh Bayly said: "The obesity problem in this country has got to such a serious state now that any action we can take we really must take.
"Around 80%-90% of television advertising is junk food advertising - food that is high in fat, sugar and salt.
"With children watching over 20 hours of television a week now it is a very, very considerable influence over their food choices."
Sue Davies, chief policy adviser to the consumer magazine Which? also backed the FSA position.
She said: "We hope that Ofcom can now accept that its approach is completely flawed and put children's health first."
However, broadcasters said such a ban could cost them £140m in lost advertising revenue.
The deadline for responses to the consultation is 30 June.
Last month, it emerged that the National Heart Forum was preparing an application for a judicial review over the consultation.
The heart charity said it was unlawful and unfair to exclude the possibility of a pre-watershed ban.