Conservative chairman Francis Maude has opened the party's annual conference in Blackpool with a stark warning they have "no God-given right to survive".
He spoke at the start of a week which will spotlight those hoping to replace Michael Howard as Conservative leader.
He said whoever the new leader is must be someone who "understands and reflects today's Britain".
And regardless of who that person was, the party had to modernise or risk extinction, Mr Maude added.
Sir Malcolm Rifkind later said the Tories must claim the centre ground, as he became the first contender to speak.
In a hard-hitting speech, Mr Maude said: "We need to offer a compelling vision of tomorrow's Britain that inspires the young who are Britain's future."
He urged party unity and an end to in-fighting.
He spoke of a single mother he met while campaigning in Crawley during the general election, who saw the Conservatives as "out of touch with how people like her live their life today".
The Conservatives should be the "natural home" for people living in cities but "too often sounded like the party of the countryside".
And the Conservatives should be the natural home for young voters but "too often we sound like people who just don't like contemporary Britain".
The Conservatives also had to reach out to families and immigrants and prove it is a party for the whole of Britain, Mr Maude told delegates.
"We can't sit back and do nothing when we're incapable of carrying our message and our purpose into large parts of the country."
The conference this week is being dominated by the contest to replace Mr Howard as leader.
Five people have so far declared they will stand. Under the election rules party members rather than MPs have the final say.
The week began with one potential candidate, Andrew Lansley, ruling himself out of the race because of a lack of support.
The party's transport spokesman Alan Duncan, who ruled out his own leadership bid in the summer, warned against parading "moral self-righteousness which had previously alienated an entire generation".
And ex-chancellor Kenneth Clarke told a fringe meeting it was a "paranoid fear" to think that he would take the UK into the euro if he became Conservative leader.
Sir Malcolm Rifkind was the first of the declared candidates to address the conference.
In a rousing speech he attacked Tony Blair and Gordon Brown and said that, although he had a mountain to climb to become leader, he believed the Conservatives could get back into government by focusing on their One Nation traditions.
David Cameron and Mr Clarke will speak on Tuesday and Mr Davis on Wednesday.
Meanwhile the fifth confirmed candidate, Liam Fox, who addresses the conference on Wednesday afternoon, told BBC Breakfast he differed from the other candidates because he cared about issues such as mental health and the breakdown of society.
"We've got a broken society in this country despite being better off, we've got higher rates of marital breakdown, higher suicide rates, higher rates of violent crime, higher rates of domestic violence - very adverse trends - that needs to be fixed."
A YouGov poll for the Daily Telegraph suggests that among Conservative voters it is a straight battle between Kenneth Clarke and David Davis.
They are tied with 30 per cent support, followed by David Cameron on 16 per cent, Liam Fox on 13 per cent, and Sir Malcolm Rifkind on 4 per cent.