In the U.S., NBC "Today" show host Savannah Guthrie said her family is ready to talk to people holding their mother, but they want to see proof that she is alive.
Guthrie said in a recorded video posted on social media that her family has heard about a ransom letter in media reports.
Nancy Guthrie was last seen Saturday around 9:45pm when she was dropped off at home by family after having dinner with them, the sheriff's department said. The 84-year-old was reported missing midday Sunday after she didn't appear at a church.
Officials said there were signs of forced entry at the home in the Catalina Foothills neighbourhood. Guthrie has limited mobility, and officials do not believe she left on her own.