David Cameron has strongly endorsed controversial comments by George Osborne in which the chancellor highlighted the killing of six children by Mick Philpott to raise questions about welfare payments.

In a BBC interview in his Witney constituency, the prime minister backed the chancellor's decision to call for a debate on whether it was right to be "subsidising lifestyles like that" – a reference to the Philpott case.

"He is absolutely right," Cameron told the BBC South of England political editor, Peter Henley. "Philpott was the one to blame for his crimes … We want to make clear welfare is not a lifestyle choice."

Cameron's intervention shows that the Tories are prepared to use the case of Philpott, who was said to have been claiming £54,253 a year through the benefit system with his partners, to reinforce a series of welfare changes that are coming into place this month. These include a £26,000 cap on household benefit claims.

On Thursday Philpott was given a life sentence for the killing of his children in a house fire. Mrs Justice Thirlwall said he should serve a minimum of 15 years in jail.

The chancellor sparked a storm of protest when he questioned the way in which Philpott had been able to claim high levels of benefits. Osborne said: "Philpott is responsible for these absolutely horrendous crimes and these are crimes that have shocked the nation. The courts are responsible for sentencing him, but I think there is a question for government and for society about the welfare state – and the taxpayers who pay for the welfare state – subsidising lifestyles like that, and I think that debate needs to be had."

Ed Balls, the shadow chancellor, accused Osborne of demeaning his office. "I believe George Osborne's calculated decision to use the shocking and vile crimes of Mick Philpott to advance a political argument is the cynical act of a desperate chancellor. For the chancellor to link this wider debate to this shocking crime is nasty and divisive and demeans his office."

The chancellor was condemned by the Liberal Democrats. Sarah Teather, the former children's minister, said: "I am shocked and appalled that George Osborne has stooped so low as to make a crude political point out of the tragic deaths of six young children. It is deeply irresponsible for such a senior politician to seek to capitalise on public anger about this case, and in doing so demonise anybody who receives any kind of welfare support."

But Philip Collins, a former speech writer to Tony Blair, warned that Labour was in danger of handing the political initiative to the Tories, as polls showed strong support for a crackdown on welfare. In his weekly column in the Times, Collins wrote: "This week the tanker of politics started to turn. The benefit cap – which limits welfare payments so that no family can receive more than average after-tax household earnings – was introduced. Housing benefit cuts began to bite.

"Then the grotesque Mick Philpott became the stooge embodiment of all that is said to be wrong with a culture in which the idle take the rise out of the working population. We may look back on this as the week in which the coalition began to speak again to the British public while the forgetful Labour party slunk back on to the sofa."

• This article was amended on 5 April 2013. The original said that Philpott was able to claim, along with his partners, £54,253 annually through child benefit. That figure is said to be the total sum claimed from benefits, including child benefit. This has been corrected.