US Today show host Savannah Guthrie says her family is “at an hour of desperation” in the search for her missing mother, ahead of a looming ransom deadline apparently set by Nancy Guthrie’s abductors.

Guthrie didn’t mention the deadline in her video, released on Monday (US time), saying she and her siblings still believed their 84-year-old mother was 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, which urged people across the US 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.”

The mysterious disappearance and search has riveted the US – from President Donald Trump who spoke with Guthrie last week to the online sleuths who’ve 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 on Thursday but a second one was set for Monday night, local time.

Law enforcement officials declined to confirm that the letters were credible but said all tips were being investigated seriously.

Authorities say they have growing concerns about Nancy Guthrie’s health because she needs daily medication.

She is said to have a pacemaker and has high blood pressure and heart issues, according to sheriff’s dispatcher audio on broadcastify.com.

Investigators returned to Nancy Guthrie’s Arizona neighbourhood several times over the weekend.

Savannah Guthrie said at the weekend the family was prepared to pay for her mother’s return.

“We beg you now to return our mother to us so that we can celebrate with her,” she said in a video posted on Saturday.

“This is the only way we will have peace. This is very valuable to us, and we will pay.”

Police remain stationed outside Nancy Guthrie’s Tucson home. Photo: AAP

Authorities believe Nancy Guthrie was taken against her will from her home just outside Tucson. She was last seen there on January 31 and reported missing the next day after not attending church.

DNA tests showed blood on Guthrie’s front porch was a match to her and her doorbell camera was disconnected in the early hours of Sunday morning, Pima County Sheriff Chris Nanos has said.

Outside the home on Monday, neighbours strolled by on their morning jogs and walks, while a county sheriff’s deputy remained stationed out front.

Detectives and agents carried out follow-up work at multiple locations over the weekend as part of the investigation, the Pima County Sheriff’s Department said on Sunday.

Investigators had not identified any suspects, persons of interest, or vehicles connected to this case, the department said.

On Sunday, an investigator was seen using a pole to search an underground tank behind Nancy Guthrie’s home.