The Department for Work and Pensions has been forced by the prime minister into reconsidering an idea it had days previously described as "not workable" as Whitehall scrambles for policies to toughen up welfare.

David Cameron wrote in a Sunday newspaper that he wanted to look at going further in welfare reforms, calling for the child benefit payments of parents who play truant from school to be withdrawn.

He suggested a more ambitious welfare reform programme when he posed the question of whether the government should be "asking much more of people on benefits who should be looking for work – or imposing even stricter penalties on those who refuse job offers?"

Research has been published by the thinktank Policy Exchange showing that some jobseeker's allowance claimants spend as little as eight minutes a day searching for work.

Ideas pushed by No 10 included measures that would force the unemployed and those claiming jobseeker's allowance to spend an entire working week in the pursuit of finding a job. But on Friday lunchtime the Department for Work and Pensions said that particular idea had been ruled out as "not workable". By Friday evening the department was instructed that the idea could be a possible candidate for tightening the welfare regime.

A Downing Street source suggested the search for stricter welfare conditionality levers was at an embryonic stage: "We're in the early stages of considering ideas and we aren't saying these ideas will definitely happen but we are trying to think how people could be helped into work."

The about-turn reflects the urgency being attached to the government going further and faster on its welfare reform agenda.

Treasury officials had also been keen on a suggestion that would see those people without a history of national insurance contributions unable to turn down suggested employment opportunities. At the moment there is a 13-week grace period in which people can claim jobseeker's allowance while they attempt to find work suitable to them and can decline Jobcentre offers. Treasury officials had wanted to close this window but a Department for Work and Pensions official said it had beendismissed as "not workable".

In his speech in his Oxfordshire constituency of Witney in the aftermath of the riots Cameron said he would like to go further on injecting greater conditionality into the benefits system – making more demanding what people have to do in order to receive benefits.

On Sunday the prime minister went further, writing in the Mail on Sunday: "What about welfare? The old something-for-nothing system we had under Labour had a poisonous effect on responsibility in our society. Again, we've already taken bold action – we're in the process of moving hundreds of thousands of people who are fit to work off incapacity benefit and are imposing sensible limits on the amount of benefit people can take. But again, given the scale of the problem, can't we go further? Say by asking much more of people on benefits who should be looking for work – or imposing even stricter penalties on those who refuse job offers?"

• The headline on this article was amended on 5 September. The original referred to "benefits cheats", which was inaccurate.