Speaking for the first time since Cho Seung-hui killed 32 people and himself on Monday, the family said it had been "living a nightmare" since the attack.
The US state of Virginia has observed a day of mourning for the victims, with vigils organised across the country.
Police say they are making "great progress" in their investigation.
The massacre was the deadliest shooting rampage in modern US history.
In a statement Cho's sister, Cho Sun-Kyung, spoke of the family's pain following the massacre.
"Our family is so very sorry for my brother's unspeakable actions. It is a terrible tragedy for all of us," she said.
On behalf of her family Ms Cho, a 2004 Princeton University graduate who works as a contractor for the US state department, expressed grief for the friends and family of her brother's victims.
We never could have envisioned that he was capable of so much violence
"We pray for their families and loved ones who are experiencing so much excruciating grief. And we pray for those who were injured and for those whose lives are changed forever because of what they witnessed and experienced," she said.
"Each of these people had so much love, talent and gifts to offer, and their lives were cut short by a horrible and senseless act."
Ms Cho said the family felt helpless, lost and shocked by her brother's actions.
"We never could have envisioned that he was capable of so much violence," she said.
Cho, 23, moved to the US with his family from South Korea in 1992.
A six-member independent panel - including former homeland security chief Tom Ridge - will examine how authorities reacted to the crisis, amid claims officials ignored warning signs that Cho, who had been admitted to a mental health unit in late 2005, was a danger.
A moment of silence was held in Virginia state at noon local time on Friday (1600 GMT), and vigils and prayers were organised across the country.
Students, staff and visitors observed a moment's silence in Virginia Tech's Drill Field and bells rang out in honour of the victims.
A similar ceremony was held in the state capital Richmond, attended by state governor Timothy Kaine.
The memorial day coincided with the eighth anniversary of the Columbine High School massacre in Colorado, in which 13 people died along with the two killers.
Also on Friday, in Israel, family members gathered for the funeral of one of the massacre victims, mathematics professor Liviu Librescu.
Cho's killing spree began at 0715 on Monday, when two people were killed at the West Ambler Johnston Hall, a university dormitory.
Two hours later Cho killed 30 students and teachers, plus himself, at the Norris Hall complex across campus.
Questions are being asked about the response to the first shootings and whether putting the campus on a full lockdown earlier could have saved lives.
Police spokeswoman Corinne Geller told the Associated Press news agency investigators hoped to have something to tell the public next week.
Last Mod: 21 Nisan 2007, 13:27