She was named tonight by Marine Police as Shani Maril.
The owner of the ferry, Niyom Pewdee, told Phuketwan tonight that the family from Israel comprised a father, mother and three children.
''The 12-year-old girl went to the toilet just before the fire broke out on the boat about 3pm today,'' Khun Niyom said. ''We hope she is found safe but there is no sign of her yet.''
The fire started in the stern of the vessel, where the toilet was located.
He said the vessel was valued at 20 million baht. All passengers were fully insured, he said.
Nine children were among the mostly-European passengers on the Ao Nang Princess 5, along with 109 adult passengers and the ferry's crew.
Tonight search boats were still scouring the sea in the hope that the girl had somehow survived.
A Royal Thai Navy vessel equipped with powerful spotlights was likely to be at the site of the sinking within hours.
Khun Niyom said that the boat burned quickly.
''Speedboats and trawlers noticed what was happening - the column of smoke went up quite high - and they came to help,'' he said.
''As a result, despite the anxiety, the passengers were taken off or plucked from the water with surprising speed. Now our thoughts are with the Israeli family.''
Khun Niyom said that the boat sank to the bottom, about 18 metres down. Divers were already conducting work by torchlight and hoped to reach the wreck overnight.
Passengers on the Ao Nang Princess 5 often used it to travel from Phuket then make day trips from Krabi to Phi Phi or other islands nearby before returning to Phuket.
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