Savannah Guthrie Shares Home Videos of Mom, Says Family Won't Give Up

Savannah Guthrie's posted a series of heartfelt home videos featuring her mom, Nancy Guthrie ... and, she says there's no way she's giving up on her mom.

The NBC journalist shared the compilation on Instagram Thursday morning ... showing her, her mom and another child who is likely her sister, Annie.

The two kids are happy ... smiling and waving at the cameras in the clip -- while Nancy beams in a bright blue dress.

A black-and-white photo shows Nancy with all three of her children -- Savannah, Annie and their brother Camron.

Savannah writes in the caption, "our lovely mom. 💛 we will never give up on her. thank you for your prayers and hope."

As you know ... Nancy was reported missing Sunday, Feb. 1, when she missed church ... hours after a family member dropped her off at her Tucson, Arizona home Saturday night, Jan. 31.

We received an alleged ransom letter which we passed on to authorities ... and the Guthrie siblings later made a video where they said they would pay for the return of their mother.

Cops detained a person of interest -- a DoorDash deliveryman named Carlos -- but they ultimately let him go. He has protested his innocence vigorously in the days since. Outside of that, law enforcement has not publicly identified a suspect or any other POIs.

Harrowing video captured a masked individual at Nancy's front door the night she was taken ... showing a man who seemed to have facial hair standing on the doorstep.