Nancy Guthrie’s family members have been cleared as possible suspects in her abduction, Pima County Sheriff Chris Nanos says, as the case involving the mother of US Today show host Savannah Guthrie enters its third week.

Ms Guthrie’s family, which includes “all siblings and spouses”, has been cooperative and gracious as authorities investigate the kidnapping, Mr Nanos said on Monday.

“To suggest otherwise is not only wrong, it is cruel,” the sheriff said in a statement.

“The Guthrie family are victims, plain and simple.”

Investigators said on Sunday they had obtained a DNA sample from a glove that was found near the 84-year-old’s Arizona home.

The glove appeared to match the pair worn by a masked man seen in doorbell camera footage before she was abducted two weeks ago, according to investigators.

Surveillance footage showing a masked person wearing a backpack, jacket and gloves in front of Nancy's front door.

The FBI has shared surveillance footage at the home of Nancy Guthrie the night she went missing in Tucson. (AP Photo: FBI)

Ms Guthrie was last seen on January 31 when she was dropped off at her home near Tucson by her family after she dined with them, authorities have said. She was reported missing by relatives the following day.

Mr Nanos has said Ms Guthrie was extremely limited in her physical mobility and could not have left her home unassisted, leading investigators to conclude early on that she had been taken against her will.

Investigators are currently consulting with Walmart management to develop leads because a backpack the suspect was seen wearing in the surveillance footage was sold at the stores, Mr Nanos said.

The suspect’s clothing “may have been purchased from Walmart but is not exclusively available at Walmart,” the Pima County Sheriff’s Department said in a statement on Monday.

“This remains a possibility only.”

No proof of life has surfaced

At least two purported ransom notes have surfaced since Ms Guthrie vanished, both of them delivered initially to news media outlets.

There has been no known direct contact between any suspects and Ms Guthrie’s family or authorities.

Traces of blood found on her front porch were confirmed by DNA tests to have come from Ms Guthrie, officials said last week.

Law enforcement and family members have described her as being in frail health and in need of daily medication to survive. She also has a pacemaker.

A sheriff places orange witches hats on a wet road at night near a sheriff's car

Police block a residential street in Tucson, Arizona, as the search for clues related to the kidnapping of Nancy Guthrie continues. (Reuters: Rebecca Noble)

Savannah Guthrie, 54, a co-anchor of the popular NBC News morning show Today, has posted several video messages, along with her brother Camron Guthrie and sister Annie Guthrie, pleading for their mother’s return and appealing for the public’s help in solving the case.

Mr Nanos has told Reuters that no proof of life has surfaced since the abduction, but added that “there’s not been any proof of death either”, saying his working presumption is that Ms Guthrie remains alive.

In an interview with the New York Post on Sunday, US President Donald Trump demanded that Ms Guthrie’s kidnappers immediately release her unharmed, suggesting he would want the Justice Department to seek the death penalty if she is found dead.

Authorities would first need to find and convict a suspect before considering sentencing.