The National Trades Union Congress (NTUC) on Monday welcomed Prime Minister Lee Hsien Loong's willingness to legislate paternity leave - one of the suggestions it made last month.
Paternity leave is now "almost a norm" in the unionised sector, said NTUC secretary-general Lim Swee Say at the last of the labour movement's National Day ceremonies this month.
"We're very happy that this may become a national norm."
During Sunday's National Day Rally, Mr Lee said paternity leave was one measure the Government was considering to boost birth rates.
The NTUC had earlier called for mandatory paternity leave of two days, along with other family-friendly measures.
But though paternity leave is a "big step", it should not be the only step, said Mr Lim.
"If the Government gives X days of paternity leave, it does not mean that the father only spends the X days to take care of the babies and the other days are the duty of the wife," he said.
Nor should fathers' involvement in parenting end once the babies grow older, he added.
Many of the 1,500 unionised companies already offer two days' paternity leave, NTUC assistant secretary-general Cham Hui Fong told reporters.
But two days is "certainly not enough", she said, which is why the NTUC has also suggested a week of paid infant care leave, to be taken by either parent.
While welcoming the prospect of paternity leave, Ms Cham tempered this with caution: "We hope that, should there be any paternity leave, it should be in addition to the 16 weeks' maternity leave that the woman is already enjoying."
What the NTUC does not want is for paternity leave to be included in those 16 weeks.
The Government may have taken one of the NTUC's suggestions on board, but it has been less open to another.
On Sunday, the Prime Minister said keeping maternity leave at 16 weeks "was about all right". The NTUC had proposed extending this to six months.
Ms Cham said that fellow female union leaders were "quite disappointed" by the Prime Minister's reaction, but noted that he had not specifically said "no".
The labour movement will continue to push the idea, not least through its ties with unionised companies, she said.
"I think we will certainly talk to the more enlightened companies to see if they can grant this."