US news anchor Savannah Guthrie has posted a video message tearfully pleading for the return of her abducted mother and seeking proof from her captors that the 84-year-old is still alive.

"We want to hear from you and we are ready to listen," the NBC host says, flanked by her siblings in the clip posted to Instagram. "Please reach out to us."

Nancy Guthrie went missing in the middle of the night from her home in the US state of Arizona over the weekend.

Authorities said they suspect she was kidnapped and they are working with the FBI to authenticate a possible ransom note.

"We are ready to talk," said the NBC host in the video posted on Wednesday night. "However, we live in a world where voices and images are easily manipulated.

"We need to know without a doubt that she is alive and that you have her."

It is standard procedure in hostage and kidnap cases for negotiators to demand proof of life from abductors. It is unclear if Nancy Guthrie's children were directed to do so by authorities.

Pima County Sheriff's Office said on Wednesday they were still speaking with anyone who had contact with Nancy Guthrie last weekend, and that no suspect or person of interest had so far been identified.

Savannah Guthrie, joined by her sister Annie and brother Cameron, said in the clip they were aware of an alleged ransom note, which was sent to at least one media outlet.

"Mommy, if you are hearing this, you are a strong woman," the Today show presenter said, her voice breaking.

"Everyone is looking for you, mommy. Everywhere. We will not rest. Your children will not rest until we are together again."

Officials have warned Nancy Guthrie could be in dire health without her medication, which Savannah Guthrie mentioned in the clip.

"Our mom is our heart and our home," she said. "Her health, her heart is fragile. She lives in constant pain.

"She is without any medicine. She needs it to survive. She needs it not to suffer."

Her sister, Annie, said the "light is missing from our lives".

"Momma," she said, "if you are listening we need you to come home. We miss you."

Shortly after the video was posted, US President Donald Trump commented on Truth Social about the case.

He said he was directing all federal law enforcement to help bring the investigation to a close and "get her mother home safely".

"I spoke with Savannah Guthrie, and let her know that I am directing ALL Federal Law Enforcement to be at the family's, and Local Law Enforcement's, complete disposal, IMMEDIATELY," he said, adding that the nation was praying for her family.

The BBC has contacted the FBI and local officials for comment.

Pima County Sheriff Chris Nanos has described an all-hands-on-deck search with dogs, drones, helicopters and federal agents to find the missing woman.

Nancy Guthrie was last seen at her home in Catalina Foothills, an affluent neighbourhood roughly six miles (10km) north-east of Tucson, on Saturday evening, when family members dropped her off around 21:30 local time.

She did not attend church on Sunday morning, which prompted members of her congregation to notify family members.

When detectives searched her home, they found a scene that caused "grave concern", Sheriff Nanos said. He refused to elaborate on what was found.

"We do believe that Nancy was taken from her home against her will. And that's where we're at," he said.

He would not comment on reports about blood found at the property.

Sheriff's officials have asked people to stop sharing misinformation about the case.

Savannah Guthrie is one of the most famous faces in US media and her video garnered support from across the media landscape and Hollywood.

The broadcast journalist, who joined NBC in 2007, was named co-anchor of NBC's Today show in 2012.

She also serves as NBC News' chief legal correspondent, and presents during the network's Thanksgiving Day programming and from the Olympics.

Savannah Guthrie had been due to co-host NBC's coverage of the Opening Ceremony for the Winter Olympics in Milan on Friday.

But she withdrew because of her mother's disappearance. Presenter Mary Carillo will take her place, NBC said.

"Our hearts go out to Savannah and the entire Guthrie family," Molly Solomon, the executive producer and president of NBC Olympics Production, said in a statement. "They continue to have our full support."

According to the Arizona Republic newspaper, a historic church in Tucson invited the community to gather on Wednesday to pray for Nancy Guthrie's safe return. (BBC)

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