In his new book, "My Father at 100," younger son Ron Reagan says signs like memory loss emerged as early as 1984. Ronald Reagan was not diagnosed until 10 years later.
Nancy Reagan has not publicly commented on her son's statements.
On Saturday, Michael stated on Twitter: "Ron, my brother was an embarrassment to his father when he was alive and today he became an embarrassment to his mother."
Appearing on CBS's "The Early Show" Monday morning, Michael Reagan said, "All these years I've listened to people like Bill Maher and other people on the left who inferred my father had Alzheimer's when he was president of the United States to somehow discount the great job my father did as president.
"So now for one of his sons to come out and in fact say, 'Yeah, he might have had Alzheimer's or he had Alzheimer's during that time,' just gives credence to people like Bill Maher and others. It absolutely offends me that somebody would say that when there's no evidence anywhere on the planet to back it up."