The father of three children found dead in their home today said the family is struggling to come to terms with the "immense and tragic" loss.
Eight-year-old twins Augustino and Gianluca Riggi and their five-year-old sister Cecilia were discovered on Wednesday at the modern townhouse in Slateford Road, Edinburgh, after reports of an explosion.
Police are waiting to speak to the children's mother, Theresa Riggi, 46, who is in a serious but stable condition in hospital after apparently falling from the second floor of the building.
The deaths are being treated as suspicious and post-mortem examinations will be carried out today.
The children's father Pasquale Riggi, who was divorcing his wife, released a statement through Lothian and Borders Police, saying: "Our family is struggling to come to terms with the immense and tragic loss of three beautiful children.
"Thanks to all who have offered such great comfort and support. We request that the media respect our privacy at this difficult time."
Police traced Shell worker Mr Riggi to the Aberdeen area after the discovery in Edinburgh, where Mrs Riggi had been living since the beginning of July.
A judge warned that the children, who were at the centre of a bitter custody battle, could be in danger just 24 hours before they were found dead.
Judge Lady Clark raised concerns about the welfare of the children after their mother failed to appear at a divorce hearing on Tuesday.
The couple were due in court today for a further hearing.
The family came from California and Colorado and Mr Riggi has worked for Shell since 1987.
He has been in Aberdeen for a number of years and in the country for 13 years.
Edinburgh City Council said it was contacted by lawyers on Wednesday regarding the recent court proceedings.
It was around the same time that the authority was told about the incident at Slateford Road.
Police hope the post-mortem examinations will determine how the children died and whether they should pursue a murder inquiry.
It was reported that the children were found stabbed to death in the flat before neighbours reported the explosion, but this has not been confirmed by police.