David Cameron’s fourth child Florence was born last August Absent fathers should be “stigmatised” by society in the same way drink-drivers are, David Cameron has said.
A father himself, Mr Cameron said “runaway dads” should feel the “full force of shame” for their actions.
Writing in the Sunday Telegraph to mark Father’s Day, he said it was not acceptable for single mothers to be left to bring children up on their own.
Meanwhile a survey has suggested men feel good at being hands-on fathers but say they are less trusted than mothers.
The prime minister also said he was determined to keep his election pledge of tax breaks for married couples.
The policy had been dropped by the coalition because of Liberal Democrat opposition.
“I want us to recognise marriage in the tax system so as a country we show we value commitment,” he wrote.
The Camerons have three children, Nancy, Arthur and Florence – who was born last August.
Their first child, Ivan, who was born profoundly disabled and needed 24-hour care, died in February 2009.
David Cameron with his father Ian at an event during the general election campaign Mr Cameron said traditional family life was the “cornerstone of our society” and called for a new drive to “bring fathers back into the lives of all our children”.
He said even when parents were separated, fathers had a duty to support “financially and emotionally” their children, spending time with them at weekends, attending nativity plays and taking an interest in their education.
Where men were unwilling to face up to their family obligations, he said that it was up to the rest of society to make clear that such behaviour was unacceptable.
“It’s high time runaway dads were stigmatised and the full force of shame was heaped upon them,” he said.
“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.”
The prime minister also talked about his admiration from his own father, Ian Cameron, who died last year aged 77.
“From my father, I learned about responsibility.
“Seeing him get up before the crack of dawn to go and do a hard day’s work and not come back until late at night had a profound impact on me,” he said.
To mark Father’s Day, a survey of 1,000 fathers – all with children aged under five – found only 15% of fathers believed their partners were more competent at caring for their baby than they were.
But 61% said they felt the general public did not trust men to care for babies as much as they trust women to.
Rob Williams, chief executive of Fatherhood Institute, the think tank which carried out the survey, said: “It is great to find out that fathers feel they are doing a good job at looking after their babies.
“It seems that this new generation of parents is well ahead of public opinion and also of public services.”
The survey also showed that nearly half said they felt they had been ignored by maternity services, while 18% said they were not aware of their right to take two weeks’ paternity leave and pay.
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