David Cameron has pledged to extend copyright on music to 70 years - in exchange for an effort by music bosses to curb violent music and imagery.
Rap star Rhymefest has condemned some violent lyrics
The Tory leader told record industry chiefs they had a responsibility to help fix Britain's "broken society".
He said censorship was not the answer - but neither was just investing in youth projects when it was the "content" of music that was often the problem.
Music did not just "reflect" culture but also created it, he added.
Mr Cameron was addressing the annual general meeting of music industry trade body The BPI in central London.
Referring to a recent Unicef report on childhood, Mr Cameron said the "single biggest challenge facing this country is that of the broken society".
He said talking about music was "very dangerous territory for politicians" but it had a far more powerful role in shaping young people's lives than politics.
He also acknowledged his own favourite artists, such as Morrissey, Bob Dylan and Johnny Cash, had not "shied away from violence in their lyrics".
And that video games, films and other forms of entertainment must also take their share of the blame for fuelling violence.
But he added: "Is some music, are some lyrics, are some videos and are some artists, helping to create a culture in which an anti-learning culture, truancy, knives, violence, guns, misogyny are glorified? Yes.
"Can we see the effects of this on our young people, in our schools and on our streets? Yes.
"Do we think we can combat this culture by government policies, policing and criminal justice alone? No."
He added: "Put simply, we have to acknowledge that all of us - as politicians, as teachers, as parents, as television producers, video game manufacturers and yes, as record industry executives - need to understand our specific responsibility in not promoting a culture of low academic aspiration or violence but instead to inspire young kids with a positive vision of how to lead their life.
Sir Cliff Richard has led calls for copyright extension
"That's why I am not calling for censorship, legislation or the banning of content.
"I am calling on you to show leadership, exercise your power responsibly and to use your judgement."
He said he had discussed the issue with Sony BMG artist Rhymefest, who has condemned some violent lyrics and met the Tory leader last year in the House of Commons.
And Mr Cameron praised schemes to encourage positive lyrics in rap music.
But he added: "When it comes to helping fix our broken society, it is not enough for the music industry to sponsor community projects.
You can make a difference by providing positive role models for young kids to look up to, draw inspiration from and aspire to be."
In exchange, he said the next Tory government would extend copyright to prevent musicians missing out on royalties in later life.
Sir Paul McCartney and Sir Cliff Richard are among the artists who will see the current 50-year limit on their early sound recordings expire soon.
But Mr Cameron said extending the length of time musicians would receive royalties from the current 50 to 70 years would also provide a "pension" for impoverished session musicians.
The Tory leader praised the music industry's contribution to the British economy and said creative industries would become increasingly important, with the end of North Sea oil and more manufacturing being done overseas.
He said a Tory government would crack down on music piracy, which was costing the UK industry more than £1bn a year.