Speaking at a rally of young Conservatives at the Young People's Parliament in Birmingham, he said Britain faced a new set of challenges.
"At the next election, there will be 18-year-olds voting who were born after Mrs Thatcher left office and a full year after the Berlin wall fell," he said. "This new generation knows that Britain faces a new generation of challenges. I want to lead a renewed Conservative Party to meet these challenges. If we change to win, we can win for Britain."
As the shadow Education Secretary formally launched his campaign to win over the party rank and file in the run-off ballot with leadership rival David Davis, his team unveiled a new slogan: "Change to Win. Win for Britain". Mr Cameron visited an urban regeneration project in Balsall Heath, promising to win back the cities for the Tories.
He said: "Conservative revival in our cities will only take place if we show how modern Conservative values are the right way to deliver a real urban revival.
"I want to set voluntary bodies and social entrepreneurs free to tackle the linked problems of family breakdown, poor school standards, crime and shoddy public space. Power to local people combined with strong leadership to ensure rigour in education and reform of the police can help deliver this revival.
"Modern compassionate Conservatism means recognising that we are all in this together and have a shared responsibility to deal with these problems."
He said: "I want the Conservatives to be a party of the cities as well as the countryside and suburbs." He also stressed that the Tory Party must attract a new generation of party activists. He will continue his campaign today with visits to the home counties and talks with Tory members of the Greater London Assembly.
Meanwhile a survey of local Tory office holders carried out by The Independent on Sunday showed that 38 of 54 local associations surveyed favoured Mr Cameron over David Davis.
The Cameron campaign already boasted more than 1,000 supporters and was boosted at the weekend by the endorsement of Lord Heseltine, the former Deputy Prime Minister.
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