The 61-year-old musician - who has been battling liver cancer - admitted he has been "very unwell" but he thinks his health is set to improve thanks to his fans' support.
Writing a blog on his official website, he explained: "I wish to thank my family, friends and fans and the many thousands of people who do not know me but have enjoyed Bee Gees music and have wished me well.
"I am very touched by your love, kindness and support. This concern from people all over the world has demonstrated the depth of feeling and love that the Bee Gees have achieved over the years.
"It is humbling and I take your prayers and good wishes for my health very seriously. I have been very unwell and am now on the road to recovery, and your prayers and wishes are a great tonic to me.
"I believe because of you I will get well and my deepest love goes out to you all. Robin xxxx"
Earlier this month, Robin was rushed to hospital after falling ill, but he was allowed to return home following five hours of treatment.