Gordon Brown has called for a "co-ordinated" effort to crack down on sales of alcohol to under-age drinkers.
Mr Brown said businesses and police had to work together
The prime minister said businesses, health workers and police had to work together to tackle the problem.
Speaking at the launch of a Home Office campaign, Mr Brown said he would look at "whether we need to do more voluntarily or in a regulatory way".
Research published by the schools watchdog Ofsted suggests a fifth of 10 to 15-year-olds regularly get drunk.
The Home Office said it is to start a campaign next month to target retailers who are selling alcohol both to under-age customers and to customers who are already drunk.
It will focus on pubs, clubs and off-licences in areas where there are high levels of alcohol-related crime and disorder.
The Home Office said the campaign would target 1,500 premises in 90 areas.
Mr Brown told a seminar in Downing Street it would look at "whether we can build upon the efforts to deal with some of the problems, particularly related to our target groups - that is young people and binge-drinkers - and whether we need to do more voluntarily or in a regulatory way".
A Downing Street spokesman said a "cultural shift" was needed.
The legal age for consuming alcohol in licensed premises is 18 unless that person is having dinner with an adult - in which case they can drink beer, wine or cider from the age of 16.
But the law allows drinking in the home from five years old.
Tesco chief executive Sir Terry Leahy said: "The evidence which we have all seen suggests that most of the alcohol consumed by young people is in their own home, probably bought by their parents.
"I think in terms of getting a clear message across, it might even help families - because young teenagers can be quite difficult to control - if they (the parents) are backed by a clear message from the law which says this is the age at which you can consume alcohol."
It has been claimed that supermarket promotions mean it can be cheaper to buy alcohol than water.
John Wright, of the Federation of Small Businesses, said: "It is more dangerous to be a small shopkeeper in London than it is to be a firefighter or a police officer. I think six were killed last year.
"When a shopkeeper is faced with a large number of youths who threaten to break his shop up if he does not sell them booze, then unfortunately, he is in a very difficult position.
"We would like to see a quicker police response."
The Downing Street seminar was attended by Home Secretary Jacqui Smith and Culture Secretary James Purnell, as well as retailers, police, academics and doctors.