Laura Bush Says Granddaughter Cora Will Be Out of NICU 'Pretty Soon, I Hope': 'She's Doing Great'

Barbara Bush's newborn baby girl is growing stronger by the day, Grandma Laura Bush said.

On Thursday's Today show broadcast, Jenna Bush Hager sat down with her mother, former First Lady Laura Bush, to update viewers on the family's newest addition. Jenna's twin sister Barbara, 39, gave birth to her first baby, daughter Cora Georgia, with husband Craig Coyne on Monday, Sept. 27, six weeks sooner than expected.

"Cora Georgia Coyne arrived a bit early, but right on time for our family, who adores her," Jenna said in voiceover during the segment.

"The baby who was supposed to be born in New York was born instead in Portland, Maine. We're thrilled with that darling little baby, and I know Barbara and Craig are too," said Mrs. Bush, 74. "I went every day to hold the baby at the hospital. So we're looking forward to the baby being able to get out of the intensive care nursery. Pretty soon, I hope."

"She's just a little tiny premature baby, but she's doing great," she added.

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RELATED: George W. Bush and Wife Laura Meet Newborn Granddaughter Cora Georgia Coyne: 'Proud and Grateful'

Mrs. Bush also shared how her husband, former President George W. Bush, reacted to being a namesake for the baby girl.

"It was really great. Cora Georgia, she'll have to be his favorite," she said with a laugh as Jenna — who shares Margaret "Mila" Laura, 8, Poppy Louise, 6, and Henry "Hal" Harold, 2, with husband Henry Hager — responded, "No! What about my children? Don't tell him that. He liked the namesake, of course."

After news of the baby's birth, Jenna celebrated on Instagram, writing: "Dearest Cora Georgia, Today is the day I got to meet my most beautiful, precious, feisty, niece (a bit earlier than we expected!)"

"I witnessed in awe as my dearest, toughest @barbara.p.bush became a mama," she continued alongside a series of photos from the hospital. "And today is the day I fell in love! Some cousins are anxiously waiting to play with you, but not just yet love. Xx auntie j"

George W. Bush/Instagram

In a recent interview with PEOPLE, Barbara said one of the "silver linings" of the pandemic was being able to stay with her parents at their Texas ranch.

"When we went to stay with my parents, we thought it would be for a handful of weeks — we didn't anticipate that it would be for the majority of a year," Barbara said. "But it's time that we never otherwise would've had, of course."

"There's something really lovely about the simplicity of being with someone every day, rather than when we normally are with our family where it's around the holidays or it's for this very condensed amount of time," she added.