TUCSON, Ariz. — As doctors gave their most optimistic assessment yet for critically wounded Rep. Gabrielle Giffords, the parents of the accused gunman in Saturday’s mass shooting broke their silence Tuesday, expressing deep sorrow for the lives lost when their 22-year-old son allegedly opened fire.

“There are no words that can possibly express how we feel,” the parents of Jared Lee Loughner said in a statement issued after days of seclusion inside their home in northwest Tucson. “We wish there were, so we could make you feel better.

“We don’t understand why this happened. It may not make any difference, but we wish that we could change the heinous events of Saturday. We care very deeply about the victims and their families. We are so very sorry for their loss.”

Giffords’ doctors, meanwhile, said her condition has improved and were upbeat Tuesday about her prognosis and that of all six victims still hospitalized.

“She has a 101 percent chance of surviving,” said Dr. Peter Rhee, trauma chief at the University of Arizona Medical Center and a former combat surgeon who worked in Iraq and Afghanistan. “She will not die.”

Rhee and other doctors now think it’s likely she was shot through the front of her head and that the bullet exited the rear, meaning the last thing she saw Saturday may have been the accused gunman taking aim with his 9mm Glock pistol.

Loughner is being held without bail on federal charges in Phoenix and may face the death penalty.

U.S. District Court Judge Raner C. Collins ordered all federal judges in the state not to participate in Loughner’s judicial proceedings because one of those Loughner is accused of killing is Arizona’s chief federal judge, John M. Roll. A judge from another state likely will preside.

The statements from Giffords’ doctors and Loughner’s family were issued on the eve of a visit by President Barack Obama to Tucson, where he will attend a memorial service this evening with U.S. Attorney General Eric Holder and Homeland Security Secretary Janet Napolitano, the former governor of Arizona.

Giffords remains in critical condition, but Rhee said Tuesday she’s able to breathe on her own, although doctors have left a tube in place to reduce the risk of pneumonia developing.

Doctors have cut back significantly on her sedation and said she’s able to make slight movements on her right side. She also has been able to follow simple commands such as moving her thumb when asked.

“I have a lot of confidence that she’s going to recover,” Rhee said, noting the “abysmal” survival rate for such wounds.

He credited the rapid response to 911 calls. Within 14 minutes, the first ambulance was on scene. Soon 11 others and three helicopters joined in, and the first patient made it to the University of Arizona trauma center within 30 minutes of the shooting.

“That’s a system that works well,” said Rhee, who was one of the first trauma surgeons sent to Camp Rhino, Afghanistan, and later created the first surgical unit in Ramadi, Iraq.