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
Addressing an audience in America, the former PM said of Europe's single currency that it was not working "as intended".
The countries lawmakers voted to impeach President Park Geun-hye in the wake of mass protests against her.
The former presidential candidate, who has herself been the target of false news reports, said such stories had 'real-world consequences'.