The family of the accused gunman in the Arizona shooting spree expressed sorrow on Tuesday over the "heinous events" while the US congresswoman who was shot in the head showed signs of improvement.
In their first public statement, relatives of Jared Lee Loughner, 22, said it was a "very difficult time" and asked for privacy.
"There are no words that can possibly express how we feel. We wish there were, so we could make you feel better," read the statement, attributed to "The Loughner Family."
The eight-sentence statement did not mention the young man charged in the shooting at a Tucson shopping mall that killed six people, including a federal judge, and injured 14 others.
The shooting left US Representative Gabrielle Giffords in critical condition but breathing on her own days after a bullet passed through her brain.
"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," the family statement said.
"We care very deeply about the victims and their families. We are so very sorry for their loss."
Giffords, a 40-year-old Democrat, was in critical condition at a Tucson hospital but is "holding her own," responding to simple commands and breathing without the aid of her ventilation tube, her doctor said.
"She has no right to look this good. We're hopeful," said Dr Michael Lemole, head of neurosurgery at the University Medical Center.
"It's week to week, month to month," he said.
"She's going to take her recovery at her own pace."
President Barack Obama plans to go to Arizona on Wednesday to attend a memorial service for the dead, which included a 9-year-old girl.
In Washington, the House of Representatives was scheduled to vote to condemn the bloody rampage that nearly killed one of their own and stirred debate about the angry politics of recent US campaigns.
Loughner is being held pending a Jan 24 preliminary hearing on five federal charges, including the attempted assassination of Giffords.
Two young men emerged from the home of the accused gunman in a middle class neighborhood of Tucson and handed out the family's statement to a throng of media waiting outside.
A neighbor earlier told local media Loughner's parents, Amy and Randy Loughner, were devastated.
"Their son is not Amy and Randy, and people need to understand that. They're devastated. Wouldn't you be if it was your child?" neighbor Wayne Smith, with tears in his eyes, told Phoenix's News Channel Three.
A CBS News poll released on Tuesday found a majority of Americans reject the view that inflamed political rhetoric contributed to the weekend shootings in Arizona.
The poll found 57% of respondents said the harsh political tone had nothing to do with the shooting, while 32% felt it did.
The rejection of a link was strongest among Republicans, with 69% feeling harsh rhetoric was not related to the attack.
While the motive for the attack was not apparent, politicians and commentators have said a climate in which strong language and ideological polarization is common may have contributed.
Former President Bill Clinton cautioned that public officials should be careful about their language.
"We cannot be unaware of the fact that, particularly with the Internet, there's this huge echo-chamber out there," he told BBC News.
"Anything any of us says falls on the unhinged and the hinged alike, and we just have to be sensitive to it."
Lawmakers in both political parties have called for greater civility in politics, and on Wednesday members of Congress will come together in a bipartisan prayer service.
Giffords' colleagues in Congress put most of their work on hold after the shootings, which prompted many of them to reassess their own security.
The Republican-led House has postponed a vote to repeal Obama's overhaul of the US healthcare system, which Giffords and other Democrats backed.
Loughner is accused of opening fire with a semi-automatic Glock pistol while the congresswoman greeted constituents in a supermarket parking lot.
"In a minute, he took away six loved ones, and took away our sense of well-being," Arizona Governor Jan Brewer said in a speech in Tucson.
"There is no way to measure what Tucson and all of Arizona lost in that moment."
More than 600 mourners gathered at a memorial service for the shooting victims at St Odilia Catholic Church in Tucson.
Arizona state lawmakers passed legislation on Tuesday to keep members of a Kansas fundamentalist Christian church from picketing at the funerals of the six shooting victims.
Brewer quickly signed the bill into law.
Members of the tiny church have gained notoriety for appearing at military funerals to declare that God had punished the troops because the United States accepts homosexuality.
The church members also turned up at the funeral of Elizabeth Edwards, wife of former presidential candidate John Edwards.