The “Today” anchor withdrew from NBC’s coverage of the Winter Games in Italy as investigators acknowledged they had few answers about who may have taken her mother, Nancy Guthrie, 84, from her home.

A woman with short brown hair sits at a TV set desk with a white wine next to her daughter, who has short blonde hair and wears a black T-shirt.
Savannah Guthrie, right, with her mother, Nancy, in 2019.Credit…Nathan Congleton/NBCUniversal, via Getty Images

As investigators acknowledged on Tuesday that they had few answers about who may have kidnapped the mother of the “Today” show anchor Savannah Guthrie, NBC Sports said Ms. Guthrie would not be part of the network’s coverage of the Winter Olympics in Italy.

The search for Nancy Guthrie, 84, who disappeared from her home near Tucson, Ariz., sometime between Saturday night and Sunday morning, stretched past 48 hours, with officials pleading for anyone who had taken her to let her go and warning that it was dangerous for her not to have her daily medication.

On Tuesday, the Pima County Sheriff’s Office said in a statement that it was “aware of reports circulating about possible ransom note(s)” about Ms. Guthrie’s disappearance after the celebrity news site TMZ said that it had received a ransom note on Tuesday demanding a Bitcoin payment. An anchor for KOLD, the CBS television affiliate in Tucson, said the station had also received a ransom note. It was not clear if the messages received by the newsrooms were actually sent by anyone involved in the abduction of Ms. Guthrie.

Chris Nanos, the Pima County sheriff, said at a news conference on Tuesday that officials did not know if Ms. Guthrie’s apparent abduction was random or targeted, or how many people may have been involved.

“We do believe that Nancy was taken from her home against her will, and that’s where we’re at,” he said.

In an interview on Tuesday night, Sheriff Nanos said the investigation would become more difficult with every hour that passes. “Time is not on our side,” he said.

Police are still working to develop suspects, and they have not yet ruled out anyone, he said. The authorities have spoken with Ms. Guthrie’s family members and they have all been cooperative, he added.

Ms. Guthrie was last seen Saturday around 9:45 p.m., when relatives dropped her off at her home in the Catalina Foothills, a quiet, wealthier neighborhood nestled under the Santa Catalina Mountains just north of Tucson.

She had been having dinner with her older daughter, Annie, and her son-in-law, who live nearby, Sheriff Nanos said. Ms. Guthrie’s son-in-law dropped her off and made sure she made it inside safely before he left, the sheriff added.

By the time police arrived the following day, officers saw “something at the home that didn’t sit well,” Sheriff Nanos said. He declined to elaborate, but said there was concerning evidence beyond red splatter on the front doorstep, which remained visible on Tuesday afternoon.

“There were things at the home that we recognized as problematic,” he said. “Inside, outside, all over.”

Sheriff Nanos said the department received a copy of a ransom note and was working with the F.B.I. to validate it. He said he has spoken with Savannah Guthrie and her security team and they are not aware of any previous threats to her or her family.

The authorities have begun to receive results of forensic tests from DNA gathered at the scene, Sheriff Nanos said, but they have not yielded any leads.

“So far nothing has come back to say, ‘Ah-ha, this is your guy,’” he said.

Savannah Guthrie, who has been away from her normal spot on the “Today” show since her mother’s disappearance, asked her followers on social media for their prayers. “Bring her home,” she wrote.

Ms. Guthrie, who joined NBC News in 2007 and joined the “Today” anchor team in 2012, was expected to be one of the most visible faces for NBC at the Olympics in Milan.

“Savannah will not be joining us at the Olympics as she focuses on being with her family during this difficult time,” an NBC Sports representative said in a statement on Tuesday. “Our hearts are with her and the entire Guthrie family as the search continues for their mother. We will share additional information about our opening ceremony coverage plans soon.”

When Ms. Guthrie did not show up at church on Sunday morning, someone from the church contacted her family around 11 a.m. A relative went to her home and found that she was missing.

Ms. Guthrie’s wallet, cellphone and vehicle were at the house, the authorities said. Ms. Guthrie has trouble moving around but is mentally sharp. She needs daily medication and could die if she does not take it, they have said.

The sheriff’s office has been inundated with tips and offers of help, Sheriff Nanos said. Big tech companies and security camera manufacturers have reached out, along with hundreds of submissions to the department’s website. Investigators are working with the company that manufactured Ms. Guthrie’s pacemaker to see whether they can gather any helpful information from it remotely.

Jon Edwards, the assistant special agent in charge of the F.B.I.’s Tucson field office, said agents were conducting interviews, reviewing cellphone information and gathering information from cellphone towers. He asked anyone who saw anything suspicious near Ms. Guthrie’s home on Saturday night or Sunday morning to call the authorities.

The sheriff’s department said it did not plan to provide additional updates until Thursday morning, unless there were urgent developments.

Many houses in the Catalina Foothills, where Ms. Guthrie lives, are on large lots surrounded by desert and vegetation including cactuses and thick desert shrubs.

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A sign propped against a cactus bearing the message: "Dear Guthrie family, your neighbors stand with you."

Nancy Guthrie’s neighbors in Catalina Foothills, an unincorporated community just north of Tucson, Ariz., showed support for her family on Tuesday.Credit…Sejal Govindarao/Associated Press

Jeff Lamie and Jennifer Michaels, who were strolling near Ms. Guthrie’s house around midday Tuesday, said they knew her only casually, occasionally seeing her out in her yard. The search, they said, had been intense, with law enforcement officials saturating the neighborhood as helicopters hovered overhead. Investigators from the Pima County Sheriff’s Office knocked on their door asking for footage from outdoor cameras.

“Obviously, this is a tragedy,” Mr. Lamie said. “We hope that she’s found safe and that she can come home.”

President Trump weighed in on Ms. Guthrie’s disappearance on Tuesday, telling reporters in the Oval Office that it was “terrible,” and saying that he planned to call Savannah Guthrie.

Nancy Guthrie had been a part of several “Today” broadcasts. In 2012, Savannah Guthrie called her mother live on her 70th birthday, and, a decade later, spoke about her mother’s “grit” in an on-air tribute for her 80th birthday. In November, “Today” broadcast a segment about Tucson, which featured Savannah Guthrie having lunch with her mother and sister.

Michael M. Grynbaum, Lourdes Medrano and Neil Vigdor contributed reporting. Susan C. Beachy contributed research.