The home secretary is considering giving police in England and Wales the power to confiscate alcohol from any under-18 who carries it in public.
Officers can currently take alcohol from youngsters in public only if they have "reasonable suspicion" they have been drinking or are going to drink it.
Jacqui Smith says she may remove this restriction to help tackle the problem.
She also said the impact on crime and disorder of 24-hour licensing laws has not been as dramatic as some feared.
Ms Smith's comments came ahead of the publication later this month of the official reviews of the impact of the Licensing Act.
The main bulk of Ms Smith's speech focused on measures to tackle under-age and binge drinking.
Ms Smith said she had written to all police chiefs reminding them not only of their powers on under-age drinking but also to stop drinking in problem areas and to close down "dodgy premises".
She said that a month-long crackdown between October and November last year in England and Wales saw officers seizing the equivalent of 6,500 pints of alcohol from under-age drinkers.
Ms Smith told BBC Breakfast: "The confiscation is certainly a campaign that we'll be running from next week and for a period of time.
"It does make a difference, because it makes it very clear that young people should not be drinking alcohol on the streets with the sort of concerns that brings to local communities and the potential for them to go on and get involved in crime and disorder."
Ms Smith also suggested that wider powers might be needed in the future: "At the moment police have to have suspicion that this alcohol is going to be used.
"I want to look at whether or not we should tighten up possession of alcohol for young people in public under the age of 18."
HAVE YOUR SAY
Alcohol-fuelled crime seems to be on the increase, so I feel Jacqui Smith's idea is a sound one
Graham Rodhouse, Helmond
The home secretary is also demanding that drink manufacturers do more to stop alcohol being sold to under-18s.
And she said she wanted to see greater use of parenting orders - to give training to tackle truancy and anti-social behaviour - for the families of people found drinking in public.
She said: "Nearly half of the alcohol obtained by young people appears to come from the family home. It's clear that parents have to hear the message as well.
"The idea that you can hand your kids a six pack of lager and tell them to disappear off for the evening - with no thought to the consequences - frankly baffles me."
Her speech was to an audience including police, local authority licensing officers, representatives from the drinks and retail industries and community groups.
Imogen Shillito, of the British Liver Trust, said people in their 20s and 30s were now getting liver sclerosis which previously would not be seen in people until they reached their 40s, 50s or later.
She also said she knew of three children under 18 who had died from liver disease.
Ms Smith said there would be £875,000 spent on the confiscation campaign starting next week and a multi-million pound Government information campaign from the summer setting out the dangers of binge drinking.
For the Conservatives, shadow home secretary David Davis accused her of making a "half-baked announcement designed to grab a headline".
He said: "The powers to confiscate alcohol from under-age drinkers on the street were proposed and passed under the last Conservative government, but ministers have no idea how effective the existing law is because they haven't the faintest idea how often it has been used.
"If the home secretary spent as much time enforcing the laws we have, as she does on media strategy, we might finally start to tackle binge-drinking on our streets and the violence that goes with it."