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.