"We are at an hour of desperation, and we need your help," she says in the video posted on Instagram on Monday afternoon.

Nancy Guthrie disappeared in the middle of night from her home in Tucson, Arizona, and was last seen on 31 January. Authorities believe she was taken against her will. The FBI is offering a $50,000 (£36,000) reward for information.

The family had earlier indicated that they would be willing to pay for her safe return. A previous alleged deadline for ransom, which is meant to be paid in Bitcoin, passed on 5 February.

Nancy Guthrie was discovered missing when she did not attend a Sunday church service on 1 February and other members grew concerned.

The family has released three previous videos saying they were willing to speak to the potential kidnapper, and asking to provide proof that her mother was alive.

"I just want to share a few thoughts as we enter another week of this nightmare," Guthrie says, appearing alone in the latest video, in contrast to previous recordings where she has appeared with her siblings. "She was taken, and we don't know where. And we need your help," Guthrie says.

She thanks the public for their prayers, saying that her mother is also feeling them "even in this darkest place".

She requests people everywhere, "even if you're far from Tucson", to report anything suspicious that could lead to clues about her mother.

She asks, "if you see anything, if you hear anything, if there's anything at all that seems strange to you, that you report to law enforcement".

On Sunday, the sheriff's office said in a post on social media that no suspects, persons of interest or vehicles had been identified in the case.

The FBI says it is looking into several ransom notes sent to local media outlets. A previous alleged deadline for ransom, which is meant to be paid in Bitcoin, passed on Thursday.

'We will pay': Savannah Guthrie's new message about missing motherAt a news briefing last week, FBI Special Agent Heith Janke said his agency was reviewing a ransom note sent to several media outlets.

The note gave a deadline for payment of 17:00 on Thursday, he said, without specifying which time zone, and had a second deadline for Monday.

On Monday, FBI Director Kash Patel arrived in Tucson, on a trip that was scheduled prior to Guthrie's disappearance.

Watch: Ghislaine Maxwell repeatedly invokes right to silence during depositionMore from the BBC2 hrs agoWhat we know about the abduction of Savannah Guthrie's mother It's been days since 84-year-old Nancy Guthrie disappeared in the middle of night from her home in Arizona.

Nancy Guthrie, 84, disappeared in the middle of night from her home in Tucson, Arizona, last weekend.

The disappearance of the 84-year-old mother of news anchor Savannah Guthrie has left a community searching for clues and hoping for her safe return.

Nancy Guthrie, the 84-year-old mother of an NBC News presenter, is believed to have been abducted from her home in Tucson, Arizona.

What we still don't know about the disappearance of Savannah Guthrie's motherThe BBC's Regan Morris is in Tucson, Arizona, where 84-year-old Nancy Guthrie disappeared from her home almost one week ago.