The statements followed Mr Rudakubana and Ms Muzayire giving evidence at the public inquiry into the killings.
The couple who gave their evidence via videolink, which could be heard but not seen by the public and press, both apologised to the victims’ families.
Ms Muzayire, who moved to the UK from Rwanda with her husband in 2002, said her family had come to the inquiry with “broken hearts”.
“There are no words that can ever be enough to express our grief and remorse for the children whose lives were taken or forever changed by our son’s actions,” she said.
She said there were “many things” she and her husband wished they had done differently.
“[For] our failure, we are profoundly sorry,” she added.
During his second day of evidence, Mr Rudakubana said he was “desperately sorry” for the families of the victims, and was “so ashamed” he “lost the courage to save their little angels”.
Nicholas Bowen KC, representing the bereaved families, told him: “They have complete disdain for your excuses and the manner in which you have answered questions.”
Mr Bowen was then stopped by inquiry chairman Sir Adrian Fulford, who told him: “That’s not appropriate at all.”
The girls’ parents issued their statements as the inquiry concluded its first phase. A second phase of the inquiry is expected to focus on the risk posed by young people with a fixation or obsession with acts of extreme violence.
Rudakubana, 18, is serving a minimum 52-year sentence for the murders.