Savannah Guthrie’s family has offered up to $1m for information leading to the return of her 84-year-old mother, Nancy, who has been missing since 1 February.

The NBC Today show host posted the offer in a video on Instagram Tuesday, more than three weeks after Nancy’s disappearance. “Someone out there knows something that can bring her home,” Guthrie says in the clip. “We are begging you to please come forward now.

“We still believe in a miracle.”

Still, the anchor acknowledged: “She may be lost. She may already be gone.”

Guthrie said that anyone with information about her mother’s whereabouts can anonymously call federal investigators at 1-800-CALL-FBI. She also wrote that tipsters can reach out directly to her.

Journalist John Miller said on CNN that the family made Tuesday’s offer because tips had slowed down after “flooding in at the beginning”.

Guthrie added that her family was aware that there were “millions of families that have suffered with this kind of uncertainty” previously.

As such, Guthrie’s family donated $500,000 to the National Center for Missing and Exploited Children to aid the organization’s work “in helping families who are coping with lost [loved ones] and actively looking for those who are lost”.

Nancy Guthrie was last seen at her home near Tucson, Arizona, on 31 January and was reported missing the following day. Authorities believe someone kidnapped, abducted or otherwise took her against her will.

Investigators have not publicly revealed much evidence. But drops of her blood were found on the front porch. And authorities recovered DNA from a glove 2 miles from Nancy Guthrie’s house – which also resembled one worn by a suspect in her disappearance, as spotted in surveillance video from the night she was last seen.

However, officials have since said that the DNA in question did not result in any new leads in the case.