Hunt said: "David Cameron has said that if it isn't a sugar tax then it needs to be something equally robust, but he has not taken a sugar tax off the table.
"Partly it's what food manufacturers do and that's why you have discussion about taxes on drinks. It's also what the retailers do, it's what schools do, it's what parents do."
A sugar tax was first proposed in a joint campaign led by Jamie Oliver and Sustain, which was then backed by Public Health England in its October report as a means to reducing sugar intake.
More recently, City Hall announced it was introducing a ten pence charge on all added-sugar soft drinks sold in its café. NHS England announced earlier this month in the Guardian that a sugar tax would be introduced across its hospital cafes in a bid to tackle obesity in England.