Savannah Guthrie did not mention the deadline in the video, saying her family still believes their 84-year-old mum is out there and hearing everyone’s prayers.

“She was taken and we don’t know where, and we need your help,” Guthrie said in the video posted on Instagram that urged people nationwide to be on the lookout. “No matter where you are, even if you’re far from Tucson, if you see anything, if you hear anything.”

“We are at an hour of desperation,” she said.

The mysterious disappearance and search has riveted the US – from President Donald Trump who spoke to Savannah Guthrie last week to the online sleuths who have flooded social media with tips, theories and rumours.

Multiple press outlets have received alleged ransom letters during the past week. At least one letter made monetary demands and set deadlines for receiving the money. The first deadline passed last Thursday but a second one was set for Monday evening.

Police officials declined to affirm that the letters were credible but said all tips were being investigated seriously.