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Victorian police believe a New Zealand toddler found abandoned at a Melbourne railway station on Saturday was left there by her father.
The little girl, of Asian appearance and dubbed "Pumpkin" by the police, was left by a man thought to be her father about 8am.
The pair were captured on CCTV cameras, the girl holding the hand of a man pulling a small suitcase.
The man disappeared and the toddler was found wandering around the station 15 minutes later by security staff.
Today police said they had identified the man and think he boarded a flight for the United States later in the day.
Police have confirmed that the three-year-old girl, named by police as Pumpkin as she was wearing a Pumpkin Patch top, and her father flew in to Melbourne from New Zealand last Thursday and stayed in the city for two nights. They were travelling on New Zealand passports.
A search is now on to find relations of the child and the New Zealand police and United States authorities are working with their Victorian counterparts.
So far police in New Zealand have not been able to trace Pumpkin's mother.
A police spokesman in Auckland confirmed that three addresses in the city had been visited, but the child's mother had not been found.
He said that the Auckland Central police station would probably be dealing with the investigation tomorrow and more information would be available.
Pumpkin is currently in temporary foster care with the Department of Human Services.
Department spokeswoman Chris Asquini said Pumpkin had settled in well with a foster family.
But she said the little girl spent a restless night on Saturday and was longing for her mother.
"She's predominantly asking for her mother," Ms Asquiri said. "It's not to be unexpected that she would be distressed and when she has been distressed, the carers have comforted her.
"She's been watching children's DVDs over the weekend and was giggling and laughing," Ms Asquiri said.
The child had begun speaking after two days of silence.
"I believe she is saying `yes' and `no' when asked questions, and she is asking for her mum and that's all we are aware she is vocalising at the moment," a police spokeswoman said.
Inspector Brad Shallies, from the Transit Safety Division, said officers believe the man had boarded a flight to the US on Saturday.
"Our belief at the moment is that he has left Melbourne, in fact left Australia. Our belief is that he may be travelling toward, or may now be in, the United States," Mr Shallies said.
He confirmed the girl and her father travelled to Australia on New Zealand passports.
"That would indicate they have been in New Zealand for some time. What type of travelling has been undertaken since her birth I'm not in possession of yet," he said.
"Some of our avenues of inquiry have suggested he exited Melbourne bound for the United States.
The search for answers was quite complex, he said.
"At the moment there are probably 50 or 60 scenarios but I don't know yet if anybody else was meant to be there (to meet the child) or whether they met with anybody else in Melbourne," Mr Shallies said.
"We believe the man is the girl's father but we're not 100 per cent sure.
"It is one of the most intriguing cases I have been involved in."
Mr Shallies said the man's behaviour in leaving Pumpkin alone was not something "anybody would accept or encourage".
He said Pumpkin's extended family may be in Australia and now they are trying to find her mother, who they think is in New Zealand.
- NZPA/AAP
