David Cameron has vowed "to get behind people who want to get on in life" to ensure Britain can "rise" again.
In his speech to the Conservative Party's annual conference, the prime minister admitted the economic recovery was taking longer than expected.
But he said Labour offered no credible alternative and the country could only weather the storm under his leadership.
He vowed to build an "aspiration nation" driven by individual ambition - the "doers, the risk-takers".
Taking a swipe at "intellectuals" like Labour leader Ed Miliband - who last week attempted to seize the moderate "one-nation" mantle from the Conservatives - he said: "We don't preach about One Nation but practise class warfare, we get behind people who want to get on in life".
Labour, he said, was a "party of one notion: more borrowing".
There were few light moments during Mr Cameron's 50 minute address, which he delivered from behind a lectern, as he tried to "set out a serious argument" about how Britain can get through its economic difficulties.
The Olympics and Paralympics showed that Britain could "do great things", he said, but there was a danger the UK could join other nations "on the slide".
"My job - our job - is to make sure that in this 21st century, as in the centuries that came before, our country, Britain, is on the rise.
"And we here know how that is done. It is the collective result of individual effort and aspiration, the ideas you have, the businesses you start, the hours you put in.
"Aspiration is the engine of progress. Countries rise when they allow their people to rise."
Like Ed Miliband last week, Mr Cameron eschewed policy announcements in favour of stressing how his own background had formed his political values.
He spoke about his father, Ian, who died last year. From him he had learned: "Work hard. Family comes first, but put back into the community too."
He also spoke about his disabled son Ivan, who died in 2009, saying his best moment of the summer was putting a gold medal around the neck of Paralympic swimmer Ellie Simmonds.
"When I used to push my son Ivan around in his wheelchair, I always thought that some people saw the wheelchair, not the boy," he told activists.
"Today more people would see the boy and not the wheelchair - and that's because of what happened here this summer."
He also fired the starting gun on the Conservatives' campaign to keep the United Kingdom together, saying he was going to meet SNP leader and Scotland's first minister Alex Salmond to "sort out" a referendum by the end of 2014.
"There are many things I want this coalition to achieve but what could matter more than saving our United Kingdom. Let's say it: we're better together and we'll rise together - so let's fight that referendum with everything we've got."
The Conservatives have this week stressed that the government would not deviate from its austerity plan and, while the economy was starting to "heal", further sacrifices would be needed beyond the next election.
Mr Cameron told Tory activists: "Unless we act, unless we take difficult, painful decisions, unless we show determination and imagination, Britain may not be in the future what it has been in the past.
"Because the truth is, we're in a global race today. And that means an hour of reckoning for countries like ours. Sink or swim. Do or decline."
But he also stressed his commitment to "compassionate Conservatism", saying his "mission" since he became Tory leader in 2005 was to "show the Conservative Party is for everyone: North and South, black or white, straight or gay.
"But above all to show that Conservative methods are not just the way we grow a strong economy, but the way we build a Big Society."
He also sought to address criticism - fuelled by the row over Chief Whip Andrew Mitchell allegedly calling a police officer a "pleb" - that the Conservatives were elitist and out of touch.
He told activists he did not have a "hard luck story" to tell, but stressed "I am not here to defend privilege, I'm here to spread it".
But, for Labour, shadow Cabinet Office minister Michael Dugher said: "This was a defensive speech from an out-of-touch, clearly rattled leader who cannot be the one-nation prime minister we need."