The plan proposed by the Equality and Human Rights Commission (EHRC) is aimed at helping support both parents and their children.
Under the plan, the amount of statutory paternity leave would increase from two to eight weeks at 90 per cent pay.
Maternity for women would reduce from nine to six months, but the proposals state they would be entitled to 90 per cent of their salary for the full 26 weeks.
Nicola Brewer, chief executive of the EHRC, said: "Changing the way we approach parental leave could be one way of tackling the gender pay gap.
"By supporting men to be good fathers as well as good employees, it would also help children do better at school and equips them for the world of work."
Ms Brewer said extending paternity rights would also help to support those families on lower incomes.
The commission issued results of a "state of the nation" survey which revealed that half of parents believe paternity pay should be longer, while a third want it to be better paid.
