David Cameron claims there has been a "big change" in the way the Conservatives think about poverty.
David Cameron says society needs to help eradicate poverty
In a speech to mark 25 years since the Scarman Report into the Brixton riots, the Tory leader argued poverty is not only "absolute" but "relative".
It was not just "material deprivation," but the fact that some people "lacked things others took for granted".
Labour said Mr Cameron was trying to erase the memory of child poverty under Conservative rule.
In his speech, Mr Cameron said: "I believe that poverty is an economic waste, a moral disgrace.
"In the past we used to think of poverty in absolute terms - meaning straightforward material deprivation.
"That's not enough. We need to think of poverty in relative terms - the fact that some people lack those things which others in society take for granted.
"So I want this message to go out loud and clear - the Conservative Party recognises, will measure and will act on relative poverty."
Mr Cameron is attempting to rid the Conservative Party of its "nasty party" image by adopting a more conciliatory tone on social issues.
He told BBC Breakfast: "I think there is a big change in the way that we think about poverty. Stop treating it as an issue for government, start treating as an issue for society."
But he ruled out capping high salaries and big City bonuses as way of tackling the inequality gap.
He said he did not believe "we'll make the country happier by capping the salary of David Beckham".
If the government intervened by capping salaries, businesses would move to European centres instead, he said.
He said there had to be "an element of redistribution" in economic policy, but the causes of poverty, such as mental health problems and drug addiction, also needed to be addressed.
He suggested that voluntary groups and social enterprises were very experienced in helping with such issues and should be encouraged to take a greater role.
"They are sometimes the ones that do best in tackling homelessness, drug addiction, debt."
The Work and Pensions Secretary, John Hutton, said the poorest families were on average better off now than they were in 1997 due to tax credits and Labour's New Deal, but would be harmed if the Tories made any cuts.
"David Cameron's commitment to 'fundamental' cuts to support for families would mean many more children growing up in poverty."
Campaign group Child Poverty Action welcomed Mr Cameron's stance of addressing relative poverty, but called for action.
"His whole party must embrace the importance of relative poverty or remain unacceptable to voters who saw the relentless growth in inequality when they were last in office," said chief executive Kate Green.
Mr Cameron's comments follow a call from a key Tory policy adviser for the party to ditch Winston Churchill's attitude to poverty in favour of Guardian commentator Polly Toynbee's ideas.
Ms Toynbee has written extensively on the social exclusion experienced by some in society.
Mr Clark told the Guardian the Tories should move away from just offering a safety net for those in "absolute" poverty.
They should also tackle "relative" poverty - people who were not in material need but who were too poor to participate fully in mainstream society, he said.
He said that earlier Conservative governments had made a "terrible mistake" by ignoring an "alarming" increase in relative poverty, contributing to an "atmosphere of anger and mistrust".
Mr Clark is a member of the party's social justice policy group, headed by former leader Iain Duncan Smith, which is due to report to Mr Cameron next month.