In a new video released Saturday, “Today” show co-host Savannah Guthrie said she and her two siblings are willing to pay for the safe return of their mother, Nancy Guthrie, who authorities believe was abducted from her Tucson, Arizona, home last weekend.

“We received your message and we understand,” Guthrie said in a short video posted to her social media account. “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. This is very valuable to us and we will pay.”

The latest video of Guthrie speaking and her siblings, Camron and Annie Guthrie, sitting by her side comes after local and federal authorities said Friday they’re “aware of a new message” regarding their mother’s disappearance. It’s unclear what kind of message it is.

A ransom note that investigators said they’re taking seriously included a deadline of 5 p.m. Thursday, said Heith Janke, the special agent in charge of the FBI’s field office in Phoenix. The note demanded payment in bitcoin, and if a transfer wasn’t made, then a second demand was for next Monday, Janke said.

Retired FBI supervisory agent and hostage negotiator Jason Pack said Guthrie’s video message on Saturday showed “extraordinary discipline under unimaginable grief and pressure.”

“In four days, they moved from an emotional plea, to a proof-of-life demand, to a public offer to pay,” Pack said, offering his analysis of Guthrie’s message for the possible abductor or abductors. “Every step was designed to keep the line of communication open and lower every possible barrier to Nancy’s safe return.”

Guthrie’s choice to use the word “celebrate” also stood out, Pack said. 

“That’s the language of resolution, not confrontation,” Pack told CBS News. “In any negotiation, you want to offer the other party a way to see this ending positively and peacefully for them too. That’s exactly what the family is doing.”

On Saturday, meanwhile, detectives continued to conduct searches in the surrounding area of Nancy Guthrie’s home in the Catalina Foothills of Tucson.

The Pima County Sheriff’s Department said investigators so far have not identified any suspects, persons of interest, or vehicles connected to the case. Two law enforcement sources told CBS News on Saturday that investigators are “developing good information” but that “nothing is imminent.”

The sources said Nancy Guthrie’s car was towed from the home, and that investigators were examining it for possible fingerprints and potential other clues. Investigators also removed a camera from the roof of the home.

The FBI has announced a $50,000 reward for information leading to Nancy Guthrie’s recovery or the arrest and conviction of the people involved in her disappearance.

Anyone with information about Nancy Guthrie’s disappearance is urged to call the Pima County Sheriff’s tip line at 520-351-4900.

Chris St. Peter contributed to this report.