Parents of about 340 - or 1 per cent of - Singaporean babies born in 2015 and eligible for the SG50 Baby Jubilee Gift have not registered to receive it.
But they can still ask for the gift sets while stocks last, said a spokesman for the National Population and Talent Division (NPTD).
The Straits Times had reported last Friday that parents of babies born last year and this year could also expect to receive baby gift sets, each worth $50, from the Government. The first of three versions of the latest gift set was given to some families last Saturday.
It had an interactive stuffed toy, finger puppets with an accompanying storybook, and a photo album.
The other two versions will be given later, with the authorities seeking feedback as part of a pilot phase to distribute 3,000 gift sets.
The SG50 Baby Jubilee Gift worth about $200 was given in celebration of Singapore's 50th year of independence.
It is a baby-size suitcase with eight items: a gold-plated medallion, shawl, baby sling, diaper bag, scrapbook, family photo frame, baby books and clothes.
Parents of SG50 babies were given the option to register for the gift. They could then choose to collect it at birth registration counters of maternity hospitals; at the Immigration and Checkpoints Authority; or have it delivered for free to their homes.
An NPTD spokesman said reminder letters were sent to parents before the end of the registration period on June 30 last year.
"Parents of eligible SG50 babies who missed the deadline can contact the Ministry of Social and Family Development (MSF) at firstname.lastname@example.org to request a (gift set), on a while-stocks-last basis," she said.
"In the meantime, as the items in the gift sets are of practical use, we have been distributing the remaining gift sets to families of newborns referred through the medical social work departments of our public maternity hospitals and MSF."
But these families will not get the commemorative medallion, which "remains exclusive to SG50 babies".
Marketing manager Jessy Chua, 33, has a son born in December 2015 and collected the gift set soon after.
When asked if she would advise eligible parents to collect the gift set, she said: "It contains the medallion and 10 years from now, they can show it to their SG50 kids and let it be a keepsake to remind them they were born in the year Singapore turned 50.
"But items like the baby clothes or baby sling would be of no use as the child would be at least 16 months old now."