TUC General Secretary Frances O'Grady said a "good gift" this Father's Day would be for ministers to increase statutory paternity pay rates and for employers to top it up for longer.
Ms O'Grady said: "Poor levels of financial support are preventing new dads from taking extra time off and are particularly affecting low-paid fathers who simply cannot afford to take leave.
"Extending paternity pay from two to six weeks and paying a better statutory rate would make a massive difference, as has been shown in other countries".
More top news
Sara Di Pietrantonio, 22, died in Rome on Sunday.
A vote to remain in the EU will see Brussels exert more power over the NHS, according to the Cabinet minister.
Tuesday: A cloudy, cool and dull day with outbreaks of heavy rain becoming lighter and patchier.