Conservative leader David Cameron has said it is a "disgrace" that people are sleeping on Britain's streets.
Speaking in east London, he said the Tories wanted to become the "progressive party" on social issues.
He launched the party's Homelessness Foundation, on which the heads of the UK's major housing charities will sit.
Housing minister Caroline Flint said the party's "warm words" were meaningless - as they opposed the government's house building targets.
Speaking in east London, Mr Cameron said it was important to look at the root causes of homelessness, such as poverty, mental illness, employment and housing shortages.
'Good society'
He said: "I think that it is simply a disgrace that in the fifth-biggest economy in the world that we have people homeless, people sleeping on the streets, sofa-surfers, people in hospitals."
Mr Cameron proposed greater links with the voluntary sector and offered to "hopefully put things into practice straight away" - in the "swathes" of councils and the London mayoralty won at this month's local elections.
"Three years ago or possibly less it would not have been possible to have imagined a serious attempt to tackle homelessness by the Conservatives"
He said: "I want the Conservative Party to get back to its roots. It should be as concerned with a good society as with a good economy, being a progressive party dealing with poverty and helping with disadvantage."
Among those who have agreed to serve on the foundation's advisory panel are John Bird, founder and editor of The Big Issue; Shelter's chief executive Adam Sampson; and Crisis chief executive Leslie Morphy.
The foundation will attempt to come up with solutions for thousands of families left without a permanent address.
The Conservatives' housing spokesman, Grant Shapps, said that "three years ago or possibly less it would not have been possible to have imagined a serious attempt to tackle homelessness by the Conservatives."
He added: "If we are honest, I think it is true to say that the centre-right has not led on the issue."
Shelter's Mr Sampson said it was "vital" tackling homelessness was a cross-party issue as it would take 15 years to solve the "crisis" of housing shortages, by building more homes.
But, for the government, Ms Flint said the previous Conservative government had halved capital spending on housing, and had not even counted the number of people sleeping rough.
She said the government had reduced rough sleeping by more than 70% and were investing £8bn in the next three years on social and affordable homes.
"Warm words from the Tories on housing are meaningless when they oppose our house building targets at a national level and block affordable housing development at a local level," she said.
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