His comments came as David Blunkett, the Education and Employment Secretary, floated the idea of Government cash handouts at 18 to give youngsters a start in life.
Mr Blair said in a newspaper interview he was "appalled" by last week's revelations that two 12-year-old girls in South Yorkshire have become pregnant, saying: "We have to prevent this in future".
The Prime Minister said: "We need to find a new national moral purpose for this new generation. People want to live in a society that is without prejudice, but is with rules. Government can play its part, but parents have to play their part. There's got to be a partnership between government and country to lay the foundations of that moral purpose."
Mr Blair was short on specifics but suggested that sex education could help Britain cut the number of teenage pregnancies, the highest in Europe. "You've got to make youngsters aware of the undesirability of having sex at 12," he said.
He sought to avoid John Major's mistake of calling for Britain to "go back to basics", saying his initiative "doesn't mean you revisit a whole series of old prejudices. What it does mean is this: parents have got to take responsibility for their own children. Twelve-year-old kids should not be on the streets at night."
Jack Straw, the Home Secretary, denied that Mr Blair was "preaching". He said: "Politicians cannot put their heads in the sand on this. It has nothing to do with preaching and everything to do with how we build a cohesive society founded on rights and responsibilities."
Mr Straw announced last night he was also calling on local authorities to use their powers to clamp down on anti-social families who make their neighbours' lives a misery.
He will be issuing a "sharp reminder" this week to council leaders in the wake of the premier's comments, said a Home Office spokesman.
The spokesman added that Mr Straw wanted to make sure councils "use their powers to control unruly delinquents and anti-social neighbours to the full".
But other politicians reacted sceptically to Mr Blair's comments. Charles Kennedy, leader of the Liberal Democrats, warned him not to fall into the same trap as Mr Major. "I think you've got to be careful. I think, emblazoned on all our souls should be the words `back to basics'."
Steve Norris, the former minister bidding to become Tory candidate for Mayor of London, said launching a moral crusade was "not an easy path for politicians to tread".
Jonathan Sacks, Britain's Chief Rabbi, urged Mr Blair to appoint a full- time minister for the family. "Until that is done, I'm afraid politicians are merely using rhetoric, they're not being serious," he told GMTV's Sunday programme.
Mr Blunkett's plan, which may be included in Labour's manifesto at the next general election, is aimed to give hope to children from poor families. Although all 18-year-olds would qualify for a cash bonus, the scheme would be aimed at bridging the gap between "the haves and have nots."
Mr Blunkett is worried that children growing up on run-down estates will not inherit money from the property of deceased relatives, and is seeking imaginative ways to help them without resorting to old-style benefit handouts. The 18th birthday present, which could be worth thousands of pounds, would have to be spent on certain items, such as education, training or buying a house.