Fathers could be offered men-only relationship classes around the time of a baby's birth to encourage them to be more involved as they grow up.
The Department for Work and Pensions is piloting the idea as part of routine antenatal classes in six areas with high rates of lone parent households.
It cites research claiming 16-year-olds today are more likely to own a smart phone than live with their fathers.
Ministers say fathers' absence can only have a negative effect on society.
Work and Pensions Secretary Iain Duncan Smith says the bond between a father and his child can make a real difference the child's life.
He said: "The problem of absent fathers is far too common - with households left worse off and, more importantly, children left without the positive involvement of two parents in their life.
"That is why this government's welfare reforms ensure that vital action is taken to change this.
"For example, by introducing relationship support for fathers, and families as a whole. If we are serious about promoting a strong society, then we also have to be serious about seeking to support and strengthen families."
The DWP says research suggests men can be reluctant to acknowledge relationship issues and argues that a different approach is needed that is more likely to secure men's support.
It is exploring whether to offer sessions tailored for men alone. The department is also looking at how any supporting material can be made less "mother centric.
The pilots will run in Cheshire, Merseyside, North East England, Eastern England, the Midlands and London.