She went on to say her second cousin Taj is "doing a flawless job on his own".
Paris Jackson is resting at home following a brief hospitalisation that generated concerns for her welfare.
In the documentary Leaving Neverland, two men allege Jackson sexually abused them as children. The Los Angeles Fire Department confirms that the patient was transported to the hospital.
TMZ reported, based on family and law enforcement sources, that emergency officials responded to her home Saturday morning before she was transferred to the hospital and placed on a 5150 hold.
The 20-year-old Jackson, who has struggled since her father died in 2009, previously attempted suicide in 2013, but has been open about her depression.
"F**k you f**king liars", she wrote.
Fans were both relieved to see Paris tweeting about the article and infuriated by the claims, with thousands reacting on social media.
The model and aspiring musician also revealed that she had purchased a new acoustic guitar.
Paris strenuously denied the latter on Twitter, saying she was photographed re-enacting a movie scene with her boyfriend for their friends' entertainment, and they were mock arguing. The report also mentioned that Jackson had maintained her father's innocence following the explosive documentary.
The collection was shown in January at the Paris Fashion week and is due to hit stores in June, but a Louis Vuitton spokeswoman said the Jackson-themed items would not be put up for sale.
If you are anxious about your or someone else's mental health, the best place to get help is your GP or local mental health provider.