David Cameron has vowed to devote much of his time in office to "an all-out assault on poverty", in his speech to the Conservative Party conference.
The prime minister, who will stand down before the next election, said he wanted to tackle "deep social problems" and boost social mobility.
He also announced "dramatic" planning reforms to increase home ownership.
And he launched a broadside at Labour leader Jeremy Corbyn, accusing him of having a "Britain-hating ideology".
Mr Cameron said he wanted his time in power to be remembered as a "defining decade for our country.. the turnaround decade... one which people will look back on and say, 'that's the time when the tide turned… when people no longer felt the current going against them, but working with them'."
- Promised to end discrimination and "finish the fight for real equality"
- Said he would not "duck" a fight over EU reform ahead of the UK's membership referendum, saying he had "no romantic attachment to the European Union and its institutions"
- Vowed to tackle "big social problems" including extremism and "segregation" caused by faith schools
- Condemned "passive tolerance" of female genital mutilation and forced marriages
- Defended the decision to launch a drone attack that killed two British Islamic State jihadists, saying he had taken "decisive action to keep Britain safe - and that's what I will always do"
- Prompted a standing ovation with praise for London mayor Boris Johnson
In his speech, Mr Cameron appealed to the centre ground of British politics, with a long section on equality, and said the Conservatives would "keep our head as Labour lose theirs".
Britain has the lowest social mobility in the developed world, Mr Cameron said.
"Here, the salary you earn is more linked to what your father got paid than in any other major country," he said.
"I'm sorry, for us Conservatives, the party of aspiration, we cannot accept that."
He got a standing ovation from Conservative members for a strongly-worded attack on Jeremy Corbyn, telling them: "We cannot let that man inflict his security-threatening, terrorist sympathising, Britain-hating ideology on the country we love."
The PM referenced remarks made by Mr Corbyn in 2011 about the death of Osama Bin Laden, when he said it was a "tragedy" the al-Qaeda chief was killed rather than being put on trial.
Mr Corbyn had gone on to describe the attack on the World Trade Centre, wars in Afghanistan and Iraq and the death of Bin Laden as tragedies, arguing "the solution has got to be law not war".
The PM accused Labour of giving up "any sensible, reasonable, rational arguments on the economy".
"It's not just that their arguments are wrong, it's the self-righteous way they make them," he said, adding: "Labour ideas don't help the poor, they hurt the poor."
Labour responded to the attacks by saying they were "a sure sign" the PM was "rattled" by Labour.
Analysis by Laura Kuenssberg, BBC political editor
'Project Camborne', for this is the plan of George Osborne as well as David Cameron, is well and truly under way.
Occupy the Labour Party's former ground while it is consumed by its own issues and moving to the left.
David Cameron made promises on equality, poverty, improving the lives of children in care, getting rid of discrimination in all its forms from the platform today. There were profound echoes of his early "compassionate conservatism".
It is impossible to imagine that at a Conservative conference a decade ago the audience would have leapt to its feet to applaud the idea of equality, yet that's what has just happened in Manchester.
It is possible however to imagine a different leader, Tony Blair, giving a very similar speech in that same era.
Mr Cameron vowed to press ahead with replacing Britain's nuclear weapons - another announcement that went down well with Tory delegates.
And he devoted a significant section of his speech to tackling "discrimination" against gay people and ethnic minorities - pointing out how CVs with white-sounding names got a better response - saying "you cannot have true opportunity without equality".
He vowed to tackle "extremism in all its forms, the violent and the non-violent" and end "segregation," telling madrassas and other faith schools that children should be "having their minds opened, their horizons broadened" rather than being taught "not to mix with people of other religions".
He also addressed criticism of his response to the Syrian refugee crisis, saying: "If we opened the door to every refugee, our country would be overwhelmed."
He hailed justice secretary Michael Gove's plans to reform the prison system to reduce re-offending - and announced a relaxation of planning rules to boost home ownership.
"When a generation of hard-working men and women in their 20s and 30s are waking up each morning in their childhood bedrooms - that should be a wake-up call for us," Mr Cameron told the audience.
Under the plans, builders in England will no longer be forced to offer low-cost rented homes in new developments.
Instead they will be able to offer "starter homes" for first-time buyers under 40 as well, at discounted prices.
The price of the "starter homes" after the discount is applied will be capped at £250,000 and £450,000 in London - and those who buy them will be prevented from selling them for a quick profit under the new policy, which aides say will provide 200,000 new homes by 2020.
Buyers will be prevented from selling them on for up to five years.
Fears the latest extension of the scheme would simply lead to a boom in "buy-to-let" properties were dismissed by Mr Cameron's aides, who said first-time buyers would not be able to get the kind of mortgage needed for property speculation.
But the chief executive of homelessness charity Shelter, Campbell Robb, said the announcement meant starter homes costing up to £450,000 would be built "at the expense of the genuinely affordable homes this country desperately needs".
Reacting to Mr Cameron's speech, SNP deputy leader Stewart Hosie said the PM's policies were "hurting the very people he professes to be helping", pointing to government plans to cut tax credits.
Lib Dem leader Tim Farron said Mr Cameron was "a seasoned PR man" whose "11th-hour conversion to social justice will fool no-one", and UKIP leader Nigel Farage said the PM had said "nothing concrete about the EU".
The Muslim Council of Britain said it was "concerned" by Mr Cameron's comments on madrassas, asking for evidence to back up the "serious allegations".