Fans from all over the world left hundreds of messages of support and wishes for the star’s swift recuperation on his Facebook page.
Emily Harrison, from Nova Scotia, Canada, wrote: “Get well, Robin, we don’t want to lose another Bee Gee!! All your fans are thinking positive thoughts.”
Robin-John, 29, had been due to premiere a collaborative classical work, The Titanic Requiem, with his father last week, but the event went ahead without Mr Gibb due to his poor health.
Other family members, including brother Barry, 65, daughter Melissa, 37, and son Spencer, 39, were also reported to have visited Mr Gibb, who is suffering from cancer and pneumonia.
Mr Gibb had surgery on his bowel 18 months ago for an unrelated condition, but a tumour was discovered and he was diagnosed with cancer of the colon and, subsequently, of the liver.
Mr Gibb’s twin brother and bandmate, Maurice, died from the same condition that initially led doctors to operate on Robin.