The 71-year-old star was close to his fellow comedian - who tragically committed suicide last month - and he admitted the two friends "never stopped" showing their affection for each other, even near the end of the 'Hook' actor's life.
He told the Sunday Telegraph newspaper's Seven magazine: "We told each other we loved each other. I told him and he told me many times ... I never stopped it and he never stopped telling me.
"As a matter of fact, I thought afterwards he tried to say goodbye to me, because he got very luvvie towards the end. It's fanciful, but that's what I told myself.
"On the last phone call he said, 'I love you like a brother' and I said, 'I know you do' and he said, 'Are you sure you know?' and I said, 'Yes'. Robin worried about everything."
The two stars were close friends and bonded over their respective battles with Parkinson's Disease, and Billy described him as "a joy".
He added: "He was my pal. He was not always depressed. He was a complicated man, but a beautiful person.
"He was a joy ... We used to talk about Parkinson's a lot. He would call me and we would compare notes. His was early onset, the same as mine. Everybody worries about it. It's like a mugger following you around."