The TV news anchor Savannah Guthrie issued a fresh appeal to anyone who knows the whereabouts of her missing mother, saying that “you’re not lost or alone” and “it is never too late to do the right thing”.

The Today anchor, who is stepping away from NBC’s morning broadcast, urged “whoever has her or knows where she is” to come forward, but did not make reference to any ransom demands or communication with any abductor.

“It’s been two weeks since our mom was taken. And I just wanted to come on and say that we still have hope. And we still believe,” Savannah, 54, said in a post to Instagram.

She appeared in the video alone, unlike in previous ones in which her siblings joined her.

The search for Nancy Guthrie, now in its 15th day, is following avenues of investigation related to the discovery of a glove found two miles from the missing 84-year-old’s home.

The FBI said on Sunday that the glove resembled those worn by Guthrie’s presumed abductor in surveillance video recorded by a camera on the night of her disappearance.

The federal crime agency said the glove carried an unknown man’s DNA. The genetic code will now be placed in a crime database, but if no match is made it will probably be entered into commercial genealogy databases.

The Pima county sheriff’s department, which is leading the investigation, has not given an official update since Friday when it announced law enforcement activity in the area. There have been no arrests and the department earlier said it was operating under the belief that Guthrie is alive.

Early on Monday, Donald Trump posted to social media about an interview that a former FBI agent, Nicole Parker, had given to Fox News, saying Parker “is doing a great job of explaining” the investigation. Parker was early in casting doubt on whether Guthrie’s disappearance was indeed an abduction.

But the Pima county sheriff, Chris Nanos, has reportedly also ruled out a circulating theory that Guthrie’s disappearance was a burglary gone wrong. Nanos told the Daily Mail that although he understood why there was public speculation around Guthrie’s son-in-law Tommaso Cioni, he didn’t want to put “a mark on somebody who could be completely innocent”.

“I understand the pundits are out there. They’re gonna say, well, he’s the last one to see her alive. We understand that stuff. But, my goodness, you’re putting a mark on somebody who could be completely innocent. And more important than that, he’s family,” he said.

“People out there can get pretty ugly and mean and nasty and not have the facts.”