In a direct challenge to Ed Miliband's attempt to claim the centre ground, he used his keynote speech to his party's annual conference in Birmingham to outline his vision of an "aspiration nation".
He said the UK had the ability to defeat its economic problems if it rewarded those who worked hard and played by the rules.
He pledged to tackle evils including idleness and said his party would do more to get young people onto the housing ladder.
In a move clearly designed to hit back at accusations earlier this week that the Tories were not doing enough for so-called strivers, he also promised to back aspiration all the way.
Just days after Mr Miliband refashioned his party as one nation Labour, Mr Cameron said it was only the Conservatives who knew "how to win, for all our people".
Labour was failing to offer voters an answer to the flagging economy, the Tory leader said.
It was not a party of one nation, he said, but rather of "one notion: borrowing".
In a section of the speech that had been extensively trailed he did not hold back from delivering a gloomy message on the economy.
Some countries may not return to the prosperity they enjoyed before the 2008 banking crisis, he warned, and the UK was facing its "hour of reckoning".
The choice was stark, he said: "Sink or swim. Do or decline."
But he also set out a vision of hope, claiming the Conservatives were the party that could ensure Britain was once again on the rise by unlocking potential "in each and every one of our citizens".
Cuts to welfare and controversial reforms to education and the NHS were designed to ensure Britain had the drive to take on the rest of the world, he said. And he hit back at claims the Tories were once again the nasty party.
He wanted to help people, he told the hall, but, unlike others, his party knew the only way out of poverty was work.
During a highly personal speech, he also credited his late father for helping to mould his political ideas.
But he refused to apologise for his privileged upbringing as the son of a stockbroker educated at Eton. He said: "I went to a great school and I want every child to have a great education. I'm not here to defend privilege but to spread it."
During his 50-minute address he also reiterated his belief that nothing could matter more than saving the Union.
He accused First Minister Alex Salmond of disliking the way this summer's Olympics had united the UK.
And he issued a call to fight the independence referendum "with everything we've got".
Scotland's Deputy First Minister Nicola Sturgeon said he had "entirely failed to talk about what is best for Scotland, revealing the fact that the anti-independence campaign is all about what is best for Westminster".
Meanwhile, Labour said the Prime Minister had obviously been "rattled" by Mr Miliband's speech to his party conference last week.
Michael Dugher, the party's Shadow Cabinet office minister, said: "This was a defensive speech, from an out of touch, clearly rattled, leader, who cannot be the One Nation Prime Minister we need."
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