The prime minister had said "runaway dads" should be "stigmatised" in the same way as drink-drivers.
Writing in the Sunday Telegraph to mark Father's Day, the prime minister said fathers who failed to "financially and emotionally" support their children must face consequences.
He said: "We need to make Britain a genuinely hostile place for fathers who go AWOL. It's high time runaway dads were stigmatised, and the full force of shame was heaped upon them. They should be looked at like drink drivers, people who are beyond the pale. They need the message rammed home to them, from every part of our culture, that what they're doing is wrong – that leaving single mothers, who do a heroic job against all odds, to fend for themselves simply isn't acceptable."
But charity Gingerbread - which campaigns on behalf of single parents - criticised the Prime Minister and said government proposals to charge those needing state help to obtain child maintenance would make life harder for lone parents.
Fiona Weir, from the charity, said: "David Cameron is right that single mums - and indeed single dads - do a heroic job, but those same parents are about to have government support ripped away from them if they need help securing child maintenance payments from their child's other parent.
"If the prime minister really wants to support heroic single parents, he must withdraw these damaging proposals which would limit access to the CSA [Child Support Agency]."
Since 2008 - when the much-criticised CSA was effectively axed - the Child Maintenance and Enforcement Commission (CMEC) has collected money from non-resident parents.
But earlier this year, the government said it wanted to encourage separating couples to organise their own payments and was proposing to charge those who did not for accessing the services of the CMEC.
They would be required to pay an upfront fee of £100 (or £50 if they claim benefits), plus an ongoing charge of between 7 of the money paid.
Labour shadow home secretary Yvette Cooper said Mr Cameron's words were "hollow".
"His government is making it much easier for deadbeat dads to run from their responsibilities by charging mums to use the Child Support Agency," she said.
Mr Cameron also said he was determined to introduce tax breaks for married couples - despite Liberal Democrat opposition to the idea.
But Ms Cooper said such a policy would "reward runaway dads who remarry".
Erin Pizzey, the founder of the first UK's women's refuge, said Mr Cameron was displaying a lack of understanding about the reality of family break-ups.
"There are a lot of reasons why [fathers are] not with their children... not least that women won't let them," she said.
Ms Pizzey said it was wrong to single out men, adding: "There is a vast mass of women who are equally as feckless as the men and we never talk about them."
Bob Greig, from the single parenting website Only Dads, agreed that the prime minister's argument was "too simplistic".
"There are many cultural, employment, financial, [and] legal issues as well which prevent dads from having a full-on relationship with their children post-separation and divorce," he told the BBC.
"Why that isn't recognised in his article in the Telegraph I just don't know."
The Camerons have three children, Nancy, Arthur and Florence. Their first child, Ivan, who was born profoundly disabled, died in February 2009.
What do you think?
Is Cameron's view too simplistic?
Are all single parents and separating couples going to be penalised by the Government?
More:Advice And Health
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