Dubai's royal family says Princess Latifa is "being cared for at home" after the BBC obtained videos in which she accused them of holding her hostage since she tried to flee in 2018.
"She continues to improve and we are hopeful she will return to public life at the appropriate time," said a statement from the royal family.
In the secretly recorded videos, the princess said she feared for her life.
The footage prompted global calls for a UN investigation.
The UN human rights agency has asked the United Arab Emirates (UAE) to provide proof that the princess is still alive.
But there was no video or photograph released with the family's statement which could serve as proof of life.
"In response to media reports regarding Sheikha Latifa, we want to thank those who have expressed concern for her wellbeing, despite the coverage which certainly is not reflective of the actual position," the family said in a response which came via the UAE embassy in London.
"Her family has confirmed that Her Highness is being cared for at home, supported by her family and medical professionals."
Princess Latifa's father, Sheikh Mohammed bin Rashid Al Maktoum, is one of the richest heads of state in the world, the ruler of Dubai, and vice-president of the UAE.
