Tucson, Arizona (CNN) -- Shot in the head less than a week ago, U.S. Rep. Gabrielle Giffords continues to make positive progress, her husband and doctors told CNN in exclusive interviews on Thursday.
The chief of neurosurgery at Tucson's University Medical Center said that Giffords' eye movements suggest the congresswoman is experiencing "glimmers of recognition."
"That tracking of the eyes tells you a whole lot more, that she's aware of her surroundings to some extent," Dr. Michael Lemole told Dr. Sanjay Gupta, CNN's chief medical correspondent. "She's trying to engage that reality."
Giffords opened her eyes briefly for the first time Wednesday, with her husband, her parents and other members of Congress in the room, and continued to open them on Thursday.
"It was extraordinary," said Sen. Kirsten Gillibrand, D-New York, who was holding Giffords' hand when she opened her eyes on Wednesday. "It was a miracle to witness."
The incident occurred shortly after President Barack Obama had visited Giffords in her hospital room.
"I think she realized the president of the United States was there, but I'm not sure she knew why," Mark Kelly, Giffords' husband, told CNN Thursday in an exclusive interview.
Giffords' breathing tube could be removed as early as Friday, Kelly said.
Less than an hour after his Wednesday visit, given permission to disclose the information by Kelly, Obama electrified a memorial-service crowd and a national television audience by revealing one of the most promising pieces of news about Gifford's condition to emerge since an assassination attempt against her on Saturday.
Giffords was squeezing and stroking Gillibrand's hand, as doctors previously said she had been able to do.
Giffords "absolutely could hear everything we were saying," Gillibrand said. "And Debbie (Wasserman Schultz, D-Florida) and I were telling her how much she was inspiring the nation with her courage, her strength, and we were talking about the things we wanted to do as soon as she was better."
Gillibrand mentioned having another night out with Giffords and her husband for beer and pizza. And Wasserman Schultz recounted telling her, "Come on, you've got to get better, because we expect you up in New Hampshire this summer" at Wasserman Schultz's vacation home.
"And just as I said that, that's when she suddenly was struggling to open ... her eyes," Wasserman Schultz said. "First just a little bit. And the doctors couldn't believe it. They said, 'This is such a good time.' "
Kelly saw her struggling, Gillibrand said, and he and the others began to encourage her, saying, "Open your eyes, Gabby. Open your eyes."
And Giffords did. Her right eye remains bandaged, but Giffords is opening both of them, doctors said Thursday
"She took a moment to focus, you could see she was focusing," Gillibrand said. "And then Mark said ... 'Gabby, if you can see me, if you can see me, give us a thumbs-up ... She didn't only give a thumbs-up, she literally raised her entire hand."
But Giffords didn't stop there, Gillibrand said. She reached out and grabbed her husband "and is touching him and starts to really choke him like she was really trying to hug him." He asked her to touch his wedding ring, "and she touches his ring, then she grabs his whole watch and wrist and then the doctor was just so excited, he said, 'You don't understand ... this is amazing what she is doing right now and beyond our greatest hopes.' "
"It was, as you can imagine, a glorious moment," said House Minority Leader Nancy Pelosi, who was also in the room.
Of the six patients the hospital is still treating from Saturday's shooting, Giffords is the only one in critical condition. Four others are in fair condition, and the sixth was being released from the hospital Thursday, said Dr. Peter Rhee, medical director of the University Medical Center's trauma center.
Giffords remains in critical condition because doctors are worried about her losing ground, said Lemole.
Giffords' doctors spoke exclusively to CNN Thursday about the first moments after her arrival at the hospital.
"My first response was I grabbed her hand, leaned into her an said 'Ms. Giffords, you're in the hospital, we're going to care for you, please squeeze my hand' and she did," said Dr. Randall Friese, a trauma surgeon.
"I got the impression that she was trying to communicate but was frustrated by the fact that she couldn't communicate," he said.
In some of his first public comments since Saturday's shooting, Giffords' husband told CNN he was in Houston when he got a call saying that his wife had been shot. Worried that a commercial flight would take too long, Kelly, a NASA astronaut, flew in a friend's plane to Arizona and met Giffords in the intensive care unit after surgery.
A 9-year-old girl, Christina Green, and Arizona's chief federal judge, John Roll, are among the dead, along with Gabe Zimmerman, a Giffords staffer. A funeral mass was held for Green on Thursday.
Also Thursday, first lady Michelle Obama released an open letter to parents about the shooting.
"In the days and weeks ahead, as we struggle with these issues ourselves, many of us will find that our children are struggling with them as well," she wrote. "The questions my daughters have asked are the same ones that many of your children will have -- and they don't lend themselves to easy answers."
"But they will provide an opportunity for us as parents to teach some valuable lessons -- about the character of our country, about the values we hold dear, and about finding hope at a time when it seems far away," the first lady continued.
Authorities say Giffords was the target of the shooting. Twelve other people suffered gunshot wounds, the Pima County Sheriff has said, while others were injured trying to flee the scene.
Tucson resident Jared Lee Loughner, 22, is facing federal charges in the attack.
A bag that is believed to belong to Loughner contains the same kind of ammunition as was used in Saturday's massacre, authorities said Thursday.
Even when Giffords' prognosis was grim, she has consistently defied the odds and met or exceeded expectations.
The next step, doctors told reporters Thursday, is the removal of Giffords' breathing tube. She is breathing on her own "with very little support," Rhee said, but he wasn't sure when the tube might come out.
Giffords is "becoming more and more alert at this time," he said, telling reporters she acts like someone waking up in the morning -- yawning and rubbing her eyes.
She has been opening her eyes more often since Wednesday, Lemole said. "This is all very encouraging," he said. "... It is a significant move forward."
Rhee said Giffords has been undergoing physical therapy, in which staffers sit her up with her legs dangling off the side of the bed. When asked, she can move both legs, straightening them out, he said.
Safeway, which owns the grocery store where the shooting took place, took out a full-page ad in Tucson's Arizona Daily Star newspaper Thursday, saying it is proud to be part of a community that cares so deeply about one another. The company is working to reopen the store, it said.
Doctors have cautiously described Giffords' recovery as going according to plan, so far absent of any complications or issues, and have said throughout that she has been able to communicate when they lessen her sedation and allow her to awaken.
Lemole said he was in the room when Giffords opened her eyes, saying it might have been the "unexpected familiarity" of having close friends visit that perhaps Giffords wasn't expecting.
"This is the part that doctors, I think, have the hardest time with -- those intangibles in medicine," he said, referring to the role that family and friends can play in prompting patient progress.
"Miracles happen every day," Lemole said. "... A lot of medicine is outside our control."
CNN's Steve Dolce contributed to this report.