Sarah Ferguson and her two daughters in Los Angeles in 2009
She said: "I want to thank you all for your kindness in supporting my family members who are going through a hard time, and we wish everyone well, every family in the world that has been diagnosed or who is going through a difficult time we wish them well.
"And of course, my brother-in-law, we wish you well, keep fighting on."
The duchess is very fond of the US and has spoke out in previous interviews about her love for the country.
The duchess previously told The Telegraph: “I will say that after I got divorced, I spent 12 years in America, writing books, and it was a wonderful place for me. I felt free there.”
She continued: “The American people have been so good to me…they really have given my babies their mummy.”