Mr Streeting also said he is considering a ban on smoking outside pubs.
He told Sky News: “We definitely want to see smoking phased out in our country, we committed to that in our manifesto.
“We want to make sure this generation of children are the healthiest generation that ever lived and therefore they will never be able to legally buy cigarettes.
“We are looking at a range of other measures to also help people who are currently smoking to quit, and also to deal with the scourge of second-hand smoke and passive smoking, which is also harmful. We’ll be setting out our proposals on that shortly.”
Asked if he will ban smoking outside pubs, he said: “Look, that’s one of the measures that I’m considering, and I’m up for a national debate on this issue.
“We have got to do two things – reform the health service, but also reform public health, because we might be living longer, but we’re becoming sicker sooner and there is a heavy price being paid for that in our economy, our public finances and in our own health.”