US news anchor Savannah Guthrie and her family have released a new video pleading for the safe return of their mother.

“We received your message, and we understand,” Guthrie said in the video posted to Instagram on Saturday evening, flanked by her two siblings. “We beg you now to return our mother to us so that we can celebrate with her.”

“This is the only way we will have peace,” she continued. “This is very valuable to us – and we will pay.” Her video did not provide any details about the message she referenced.

Nancy Guthrie disappeared in the middle of night from her home in Tucson, Arizona, last weekend. Authorities believe she was taken against her will.

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 is offering a $50,000 (£36,000) reward for information.

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

Authorities say that early on Sunday morning, a doorbell camera in her home was disconnected and removed. At about 02:28 local time, the app connected to her pacemaker, an implanted cardiac device, was disconnected from her phone.

FBI Special Agent Heith Janke has said the bureau was looking into a potential ransom note sent to several media outlets.

Reuters A notice circulated by the Pima County Sheriff’s Office requests information on the disappearance of Nancy Guthrie, showing her agem and description, along with a photo of her. Reuters

Authorities said on Friday that they were “aware of a new message regarding Nancy Guthrie” and were “inspecting the information provided in the message for its authenticity”.

Janke said the note “had facts associated with a deadline with a monetary value they were asking for”, NBC News reported.

A presenter for a local CBS News affiliate told the BBC that her channel had received the “message” but did not detail its contents.

According to news website TMZ, which reportedly received one of the letters, the kidnappers were demanding millions of dollars’ worth of cryptocurrency, which is popular with criminals and often difficult to trace.

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What we know about the abduction of Savannah Guthrie’s mother

BBC News Map of Arizona showing location of Catalina Foothills and above the map is a photo of Guthrie's home in the desert with annotations showing where her doorbell camera was removed and where the porch is with the bloodBBC News

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

In a video on Thursday, Camron Guthrie – the son of the missing woman – confirmed the family had not had any direct contact with kidnappers.

“We have to know that you have our mum,” Camron said in the family’s latest video message. “We want to talk to you.”

The FBI did arrest one individual regarding a fake ransom note on Thursday.

Family, and law enforcement, have warned that Nancy Guthrie may be at risk without her medication.

“She is without any medicine,” Savannah Guthrie said in a previous announcement. “She needs it to survive. She needs it not to suffer.”

Watch: What we still don’t know about the disappearance of Savannah Guthrie’s mother

The Pima County sheriff’s office said investigators had returned to conduct “follow-up” at Nancy Guthrie’s home on Friday as part of their investigation. They also revisited the home of Annie Guthrie, Nancy’s daughter and Savannah’s sister on Saturday, according to multiple US news outlets.

US President Donald Trump said last week that he had spoken to Guthrie and offered federal law enforcement help.

“I think we’re doing very well, meaning we have some clues, I think that are very strong and I think we could have some answers coming up fairly soon,” he told reporters on Friday.

Pima County Sheriff Chris Nanos said on Thursday that investigators were no closer to finding out who was responsible – but that they were working on the assumption she was still alive.

“Right now, we believe Nancy is still out there. We want her home,” he said. “Everybody’s still a suspect in our eyes.”

Savannah Guthrie, 54, is a US broadcast journalist who has served as the co-anchor of NBC News’ Today since 2012.

She is also the network’s chief legal correspondent and a primary anchor for its election coverage. Previously, she was NBC News’ White House correspondent.