Tucson, Arizona (CNN) -- One week after being shot through the head, U.S. Rep. Gabrielle Giffords is off the ventilator and breathing on her own through a tracheotomy tube, the University Medical Center of Tucson, Arizona, said Saturday.
Giffords, who authorities say was the target of a mass shooting by Jared Lee Loughner that left six dead and another 13 wounded, remains in critical condition. Still, in a statement, the southern Arizona hospital said that her recovery "continues as planned."
Another person wounded in the incident, 58-year-old James Tucker, was released from the hospital Saturday, according to the medical center. Two other victims are in good condition at the hospital, while others wounded had been treated and released earlier this week.
The Giffords' development is the latest milestone for a woman who was critically wounded after a bullet went into her skull, through her brain and then back out her skull.
Doctors on Saturday morning replaced the breathing tube that ran down her throat with a tracheotomy tube in her windpipe. That procedure protects Giffords' airway and allows her to breath independently for the first time since her first surgery after the shooting, the medical center said.
A feeding tube was also inserted earlier Saturday into Giffords, to make it easier for her to get needed nutrients. The hospital said that such procedures are "not uncommon" among intensive care patients suffering serious brain injuries.
Police say that a gunman -- who they claim is Loughner, a 22-year-old Tucson resident -- killed several others in a Safeway parking lot in Tucson while trying to assassinate Giffords, who was then holding a constituent meeting.
A law enforcement source said Saturday that Loughner had photographed himself posing with a 9mm handgun while wearing a red G-string.
It's not clear when the photo was taken, but it was among those on a roll of 35 mm film that Loughner dropped off at a Walgreen's store in the hours before the shooting rampage.
The Safeway where the shooting ocurred reopened Saturday morning for the first time since the incident. Store officials made a public address announcement inviting those who were in the store to step outside for the observation shortly after 10 a.m. MT (12 p.m. ET).
Some in the crowd approached flower-bedecked barricades marking the scene and placed flowers. One woman, comforted by another in a green Safeway store apron, sobbed as she attempted to place a lighted candle and a handmade card reading, "God Loves You."
A wreath was placed at the site to honor the victims, Safeway spokeswoman Susan Houghton said.
Damage to the store has been completely repaired, she said.
Dr. Michael Lemole, the hospital's chief of neurosurgery, said Friday that Giffords is "beginning to carry out a more complex sequence" of activity.
"We're confident (Giffords) is making progress now," he said. "We couldn't have hoped for anything better given the severity of (her) injury."
In a Friday Twitter post, Giffords' husband, NASA astronaut Mark Kelly, thanked his "great followers" for their support.
"GG has been improving each day," he said.
Those killed in last Saturday's attack included a 9-year-old girl, Christina Green; Arizona's chief federal judge, John Roll; and Gabe Zimmerman, a Giffords staffer.
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 the 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, Steve Dolce, Susan Candiotti, Greg Morrison and Greg Botelho contributed to this report.