Peter Fahy, of Cheshire police, said raising the limit would send "a clear message about the dangers" of alcohol.
But Home Office minister Meg Hillier said parents, not legislation, had the power to stop underage drinking.
And drinks industry body the Portman Group said 18-year-olds "should be trusted to drink".
Mr Fahy made his comments after three youths appeared in court charged with the murder of father-of-three Garry Newlove, 47, in Warrington, Cheshire.
He also said there should be a ban on drinking in public areas outdoors to help combat underage alcohol abuse and anti-social behaviour. "Alcohol is too cheap and too readily available and is too strong. Young people cannot handle it," he said.
Ms Hillier said raising the age limit would do nothing to stop underage drinkers getting access to alcohol.
"We have this attitude that it's OK to go out and get plastered, publicly and privately," she said.
"It's not something that government or legislation or the police alone can solve; it's much more of an attitude in society.
"In the end, the buck will stop with parents."
Conservative home affairs spokesman James Brokenshire also dismissed Mr Fahy's proposal, arguing the solution was to give local communities more power over the operation of licensing.
"Just having a 21-year-limit will not deal with the 11 and 12-year-olds who are binge drinking on a monthly basis and the 15 and 16-year-olds who are getting alcohol very freely," Mr Brokenshire told the BBC.
"He (Mr Fahy) does raise important issues and highlights the failure that the government has made in terms of the introduction of their own licensing laws - expanding the availability of alcohol - and also their failure to tackle the issues of family breakdown as well.
"Rather than getting the cafe culture they were promising, we are actually getting a violent crime culture."
'Blind eye' The chief constable, however, said the problem was not extended pub opening hours, but shops and supermarkets which sold alcohol to underage youths.
He also blamed parents for "turning a blind eye" to their children's underage drinking.
Drinks industry body The Portman Group, which aims to promote responsible drinking, claimed raising the legal age could lead to more unsupervised drinking by young people and an increased risk of accidents and anti-social behaviour.
Chief executive David Poley said: "If 18-year-olds are allowed to smoke, vote and go to war, they should also be trusted to drink.
"We can curb alcohol-related problems through more effective education, greater parental responsibility and tougher enforcement of the law on underage sales."
And 21-year-old Rocky Lorusso, spokesman for the British Youth Council, said Mr Fahy's comments only served to reinforce negative stereotypes about young people. "What we need is greater education and awareness of the dangers of alcohol and more safe places for young people to meet - not reactionary police powers and negative attitudes," Mr Lorusso said.
http://newsvote.bbc.co.uk/2/hi/uk_news/6948419.stm?dynamic_vote=ON#vote_drinking_age
But Home Office minister Meg Hillier said parents, not legislation, had the power to stop underage drinking.
And drinks industry body the Portman Group said 18-year-olds "should be trusted to drink".
Mr Fahy made his comments after three youths appeared in court charged with the murder of father-of-three Garry Newlove, 47, in Warrington, Cheshire.
He also said there should be a ban on drinking in public areas outdoors to help combat underage alcohol abuse and anti-social behaviour. "Alcohol is too cheap and too readily available and is too strong. Young people cannot handle it," he said.
Ms Hillier said raising the age limit would do nothing to stop underage drinkers getting access to alcohol.
"We have this attitude that it's OK to go out and get plastered, publicly and privately," she said.
"It's not something that government or legislation or the police alone can solve; it's much more of an attitude in society.
"In the end, the buck will stop with parents."
Conservative home affairs spokesman James Brokenshire also dismissed Mr Fahy's proposal, arguing the solution was to give local communities more power over the operation of licensing.
"Just having a 21-year-limit will not deal with the 11 and 12-year-olds who are binge drinking on a monthly basis and the 15 and 16-year-olds who are getting alcohol very freely," Mr Brokenshire told the BBC.
"He (Mr Fahy) does raise important issues and highlights the failure that the government has made in terms of the introduction of their own licensing laws - expanding the availability of alcohol - and also their failure to tackle the issues of family breakdown as well.
"Rather than getting the cafe culture they were promising, we are actually getting a violent crime culture."
'Blind eye' The chief constable, however, said the problem was not extended pub opening hours, but shops and supermarkets which sold alcohol to underage youths.
He also blamed parents for "turning a blind eye" to their children's underage drinking.
Drinks industry body The Portman Group, which aims to promote responsible drinking, claimed raising the legal age could lead to more unsupervised drinking by young people and an increased risk of accidents and anti-social behaviour.
Chief executive David Poley said: "If 18-year-olds are allowed to smoke, vote and go to war, they should also be trusted to drink.
"We can curb alcohol-related problems through more effective education, greater parental responsibility and tougher enforcement of the law on underage sales."
And 21-year-old Rocky Lorusso, spokesman for the British Youth Council, said Mr Fahy's comments only served to reinforce negative stereotypes about young people. "What we need is greater education and awareness of the dangers of alcohol and more safe places for young people to meet - not reactionary police powers and negative attitudes," Mr Lorusso said.
http://newsvote.bbc.co.uk/2/hi/uk_news/6948419.stm?dynamic_vote=ON#vote_drinking_age