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The family of the man accused in Saturday’s shooting rampage in Tucson, Ariz., broke its silence Tuesday, issuing a brief written statement expressing sympathy for the victims and their families.

“We don’t understand why this happened,” the family wrote in the statement distributed to a cadre of reporters assembled outside the home. “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.”

The parents of Jared Lee Loughner, the 22-year-old accused of killing six and wounding Rep. Gabrielle Giffords and 13 others, have remained in their one-floor home in a suburb of Tucson since the shooting. A neighbor told the Associated Press that they have been devastated, wondering where they went wrong with their son.

“There are no words that can possibly express how we feel," the family said. "We wish that there were (words), so we can make you feel better.”

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The family also asked for the media to respect their privacy.

Loughner, who is said to have lived at the home with his mother and father, stands accused of shooting Giffords in the head at point-blank range, then firing on the crowd assembled at a grocery store for a town hall-style event held by Giffords, whom police said was the target of the attack. The motive, however, remains unclear.

After the initial sense of shock and dismay in the community, Tucson residents have started to express sympathy for the family. A local elementary school teacher watching the commotion outside the Loughner house Tuesday said “people aren’t all blaming them,” adding that the Loughners just need support.

A neighbor, who did not wish to give her name, said the family must be “hurting real bad.”

Jed Hollenbach, the associate pastor at the nearby Grace Community Church, said the church community might soon offer counseling to the Loughner family.

"Our hearts would definitely push us in that direction," he said. "They're going to be wrestling with guilt."

He said pastors and counselors in the area will go to Safeway, the scene of the shooting, on Saturday, when the store is set to reopen, and offer counseling to employees and others who need it.

"I think the family is really wondering, is there more that we could have done?” said Hollenbach. “I imagine that it's crippling."

Earlier Tuesday, a young man walked up to the front of the Loughner house and left a card and a rose on one of their cars. The inscription on the card was made out to “Mr. Loughner.” The individual refused to say anything to news crews on the scene.

Little is known about Loughner’s parents. Most neighbors had very limited interaction with them; many did not know their names until Saturday’s shooting.

Loughner's mother has been employed by the local parks department for nearly 25 years. She started out as a maintenance worker, but worked her way up to become a park manager at Agua Caliente Park just outside Tucson. The park, a former hot springs resort more than a century ago, is a lush plot of land dotted with palm trees which surround the park’s tranquil pond – a far cry from the darkness of her home where she has apparently been spending all her time since the shooting.

Gwyn Hatcher, the Pima County government's human resources director, told Foxnews.com the county will offer grief counseling services to the Loughner family if it has not done so already. The "employee assistance program" has already been offered to other parks department employees.

Randy Loughner, the gunman's father, apparently has not worked for years, the Associated Press reported. He would, at times, fix cars at the home.

Both parents were picked up in front of their home in a Ford Mustang at 7:25 p.m. local time. As they left the house,  the two covered their heads with hoods to prevent pictures and neither acknowledged the press. It was believed that they were accompanied by their legal team.

Authorities have revealed clues the alleged shooter left behind at the home. They found a note at the home that read, “I planned ahead” and “my assassination.”

He also memorialized a letter from Giffords’ office – a thank you note for attending a 2007 event similar to the one at which police say he attended Saturday.

The suspect also reportedly wrote "Die, bitch" on another sheet of paper found inside the home. It was unclear if the message was intended for the congresswoman.

Since the shooting, doctors say Giffords has made strides in her outlook and is currently breathing on her own. One doctor gave her a "101 percent" chance of surviving the gunshot. Doctors say the extent of the injuries and the quality of life she’ll have remains unclear.

FoxNews.com's Judson Berger and Edmund DeMarche contributed to this report.