Jackson, 82, has been raising the three young children of her son, pop music icon Michael Jackson, who died in 2009.
A man identified as her nephew Trent reported her missing, saying she had not been heard from in a week. Michael's 14-year-old daughter Paris echoed the claim in a Twitter posting.
The L.A. Sheriff's Department told E! News investigators know Katherine is safe with members of her family, but are still talking to relatives to see why there are differing accounts regarding her whereabouts.
"Let me put to bed today's nonsense: as I made clear some days ago, Mother is safe and well in Arizona with her daughter and our sister, Rebbie, resting up on doctor's advice, so it is beyond me how she can be reported 'missing,'" Jermaine Jackson, Katherine's son, said during the weekend on Twitter.
"This incredulous claim was made for reasons best known to the adult/s (sic) who filed it but it seems no accident that it comes after we, the sons and daughters, put in place care-taking for our own mother, taking her to Arizona in line with doctor's advice following a check-up. Furthermore, it dismays me that such an alarmist 'missing person' report has caused unnecessary anxiety among Michael's children who will understandably react to what they misunderstand, hear or are told.
No-one is being 'blocked' from speaking with Mother. She is merely an 82-year-old woman following doctor's orders to rest-up and de-stress, away from phones and computers. Everyone has been well aware of this within the family, but I would like to reiterate my reassurance to the outside world that Mother is fine. In the meantime, thank you for all your thoughts and concerns."