The Die Hard actor, who was diagnosed with frontotemporal dementia, turns 70 on Wednesday, and his and ex Demi Moore's daughter encouraged fans to wish him a happy birthday.
When asked in an Instagram Stories Q&A session on Tuesday how Willis was doing, Rumer said: "He's doing great, thank you for asking.
"It is actually his 70th birthday tomorrow so please wish my papa a big happy birthday."
The House Bunny actor, 36, spoke in February about how her father was doing amid his battle the degenerative disease, which causes behavioural changes and communication difficulties.
Speaking on UK TV show Loose Women following the Los Angeles wildfires, she explained: "He's doing great. I think, obviously as many people in California, the thing we're all kind of the most scared, dealing with is just fires and wanting to make sure everything is OK.
"Because my family, we're all so close, I think what's so beautiful is the way that we rally around each other, (it's) so lovely, because we really are a unit."
In January, Willis's wife, Emma Heming Willis, 46, claimed her husband's stuttering was dismissed by health professionals as an early symptom of his dementia.
Speaking to Town and Country magazine, she said: "He had a severe stutter as a child. He went to college, and there was a theatre teacher who said, 'I've got something that's going to help you.'
"Bruce has always had a stutter, but he has been good at covering it up.
"So, when he began to experience difficulties with language, it seemed like it was just a part of his stutter.
"Never in a million years would I think it would be a form of dementia for someone so young."
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