Emergency services were called to Carlton Railway Station at about 12.25pm after reports the pram, carrying two twin girls, had rolled from the platform onto the path of an oncoming train.

The train was travelling city-bound from Cronulla to Bondi Junction in what has been described as an "incredibly rare" but "absolutely tragic" incident.

"The train did stop a short distance from the end of the platform so it appeared it was slowing as it headed through the station," Superintendent Dunstan said.

Premier Minns expressed his condolences to the immediate family and local community, saying the father died from "an extraordinary, instinctive act of bravery".

Trains are not running between Wolli Creek and Hurstville on the T4 Illawarra line and Carlton Railway Station remains closed.

Chief Executive of Sydney Trains Matthew Longland said he was working with police to get the rail network up and running again, and expected full services on Monday.

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