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.