Chief Executive Leung Chun-ying has asked the public to give his family breathing space after one of his daughters admitted cutting her wrists.
Leung made the call yesterday after returning from a visit with his wife to Britain, where their two daughters and son study.
Their elder daughter, 22-year-old Chai-yan, posted pictures on her Facebook page on Wednesday showing cuts to her wrist and asked: "Will I bleed to death?"
Leung, speaking for the first time since the photos emerged, said: "Every parent cares about their children … and parents would exhaust every effort to help and protect their children if they are in trouble."
Chai-yan told a Chinese-language newspaper she was "going through something".
However, she did not link what had happened to her father's high-profile job as the city's leader.
The chief executive said: "What Chai-yan needs right now is a quiet environment. It's not easy to be the daughter of a public figure.
"I hope people who care about Chai-yan could leave some space … to her and my family."
In the interview, Chai-yan said she was "manipulated" into posing for a picture last week with her parents in Hyde Park, London, which was later published on the Leung-friendly website Speak Out Hong Kong.
"I was manipulated to go to Hyde Park and play happy family as a lame PR stunt by my father," said Chai-yan, a law student at the London School of Economics. Her parents were in Britain to attend the graduation of their younger daughter, Chung-yan, at Cambridge University.
Chai-yan added: "You can say I'm the 'black sheep' of the family. I have very strong views of my own. I do not believe in a lot of my family's views."
Professor Lee Sing, an expert in psychiatry at Chinese University, said that emotional distress might shape a person's perception.
He refused to speak about Chai-yan's situation, but said: "The one who the person said they hated the most might turn out to be the one he or she loved the most."
Chai-yan's use of social media has caused controversy before.
She received thousands of angry comments in March when she wrote on Facebook that a brutal attack on former Ming Pao chief editor Kevin Lau Chun-to had nothing to do with issues of press freedom.