Read more about the Arizona shooting as CNN's Dr. Sanjay Gupta speaks with the wounded congresswoman's husband, Mark Kelly, and another victim.
Tucson, Arizona (CNN) -- U.S. Rep. Gabrielle Giffords remains in critical condition but is continuing to make progress, doctors at Tucson's University Medical Center said Friday.
Giffords is one of four victims of last Saturday's massacre still hospitalized at the center, according to Dr. Peter Rhee, the hospital's medical director for trauma. The other three patients are now in good condition, he said.
"We're confident (Giffords) is making progress now," said Dr. Michael Lemole, the hospital's chief of neurosurgery. She is "beginning to carry out a more complex sequence" of activity.
She is making "all the right moves," he noted. "We couldn't have hoped for anything better given the severity of (her) injury."
Giffords' husband, NASA astronaut Mark Kelly, in a Twitter post thanked his "great followers" for their support.
"GG has been improving each day," he said.
The Arizona Democrat was shot in the head last weekend while meeting with constituents, allegedly by 22-year-old Tucson resident Jared Lee Loughner.
Loughner faces federal charges in the attack that killed six people and injured 13 others.
Among the fatalities from Saturday's massacre: a 9-year-old girl, Christina Green, and Arizona's chief federal judge, John Roll, along with Gabe Zimmerman, a Giffords staffer.
A funeral Mass was held for Green on Thursday. Roll's service was held Friday.
Christina's father, John Green, told CNN Friday that some of his daughter's organs "went to a little girl in Boston."
"It was very poignant to find out. That's what Christina was all about," he said. "It's a blessing."
In his first interview since the tragedy, Kelly told Dr. Sanjay Gupta, CNN's chief medical correspondent, that his wife is aware to some degree of what is going on around her.
Asked if she knew that President Barack Obama had visited her hospital room Wednesday, Kelly said yes. "I think she did know ... though, I think she was trying to figure out what he was doing there," said Kelly.
One doctor was optimistic that Giffords would survive, he said, while another took a more "long-term view of the future."
"I do think about her neurological function, and it is just too early to tell what that will be," Kelly said.
Dr. Randall Friese, a trauma surgeon, recalled grabbing Giffords' hand after she arrived, telling her "we're going to care for you," then asking her to squeeze his hand -- which she did.
"I got the impression that she was trying to communicate but was frustrated by the fact that she couldn't," he told CNN in an exclusive interview.
Doctors have consistently 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.
Giffords opened her eyes briefly for the first time Wednesday, shortly after Obama visited and with her husband, 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."
Gillibrand said that she and Debbie Wasserman Schultz, a Democratic congresswoman from Florida, were telling Giffords about how she was inspiring others and discussing things they wanted to do once she got better -- like 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.
"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."
Kelly recalled the moment in the interview with Gupta.
"At first I thought she was trying to strangle me," he joked to CNN's Gupta.
Kelly had asked his wife to touch his wedding ring that night, "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.
Giffords remains in critical condition because doctors are worried about her losing ground, said Lemole.
Sens. John McCain and Jon Kyl of Arizona plan to introduce legislation to name a new federal courthouse in Yuma, Arizona, after Roll.
Roll approved the building plans for the courthouse, according to McCain aide Brooke Buchanan.
Shooting victim Ron Barber, a Giffords' aide, was released from the hospital Friday. Fellow aide Pam Simon got out of the hospital Thursday.
"My healing process is well under way," Barber said in a statement read by family members.
"There are a lot of wounds (but) the wounds in our heart are a lot deeper," Simon said. "They're not going to heal for a long, long time -- if ever."
Former Justice Sandra Day O'Connor, an Arizona native, released a statement Friday urging "civility and rationale dialogue" in the wake of the shooting.
"As we grieve, we must not allow these events to further divide our state and our nation," said the 80-year-old retired justice. "We must reject violence and hostility and bring civility and rational dialogue into our government and our community life. This is a responsibility of every one of us as individuals. Only we -- working together -- can restore reason and civility in our public speech and actions."
Meanwhile, the investigation into the attack continued as authorities on Friday released a detailed timeline of Loughner's activity in the hours before the shooting. A day earlier, they found a bag that is believed to belong to Loughner and contains the same kind of ammunition as was used in Saturday's massacre.
DNA testing on the bag, which contained seven boxes of 9mm ammunition, could take up to 10 days before the results are determined, according to Pima County Sheriff's Department Capt. Chris Nanos.
CNN's Alan Silverleib, Bill Mears, Ted Barrett, and Steve Dolce contributed to this report.