By Jack Gramenz in Sydney

Safety upgrades for train stations will be considered after a father and his toddler daughter died when a pram rolled onto the tracks.

The girl’s surviving twin and mother have left hospital after the tragedy at Carlton railway station in Sydney’s south on Sunday afternoon.

The two-year-old was heard crying from under a train after the pram fell onto the tracks, prompting their father to try in vain to save his daughters from an oncoming train.

The 40-year-old man and one of the twin toddlers died at the scene.

NSW Premier Chris Minns said the man made an instinctive and heroic effort to save his children.

“It’s devastating for that family … I can only imagine what they’re going through,” he told reporters on Monday.

Multiple investigations into the horrific incident – including a coronial inquiry – would identify any necessary changes to improve safety.

But Mr Minns said he would not immediately commit to any measures, such as the installation of glass barricades used on metro stations, until he knew how they could be implemented.

“We will take steps that we need to take to keep people safe,” he said.

“Unfortunately, public transport, particularly train stations, can be dangerous and it’s incumbent upon everybody to be as safe as possible.”

The surviving toddler fell between the tracks and was miraculously left without serious injuries.

She and her 39-year-old mother, who was traumatised after seeing the disaster unfold, have been discharged from St George Hospital.

Sydney Trains chief executive Matt Longland said the train, which was not due to stop, had approached the station with caution as drivers were instructed to do, but its speed would form part of an investigation into the incident.

All the relevant information, including CCTV footage from the station, had been handed over to police, he said.

The National Rail Safety Regulator has been notified and a report will be prepared for the coroner.

NSW Police Superintendent Paul Dunstan said the father of the twins went into “parent mode” after their pram rolled in front of the train.

“In doing so, it’s cost him his life, but it’s an incredibly brave and heroic act by the dad,” he said on Sunday.

The girl who survived was saved by “good luck more than anything”.

“The police that climbed under the train said that she was sort of in between the tracks, the way that she’d fallen, and she was largely untouched,” he said.

The mother was being supported by friends and family and the local Indian community.

“But she’s clearly in a state of shock and struggling with what’s happened,” Supt Dunstan said.