The comments came days before the one-year anniversary of Reeva Steenkamp's Valentine's Day death and ahead of Pistorius's March 3 trial on charges of murdering the model and aspiring actress.
"June and other family members will be at the trial in Pretoria. All we are looking for is closure and to know that our daughter did not suffer on that tragic Valentine's Day," June and Barry Steenkamp said in a statement.
Pistorius, 27, whose legs were amputated below the knee when he was a young boy, shot to fame as the "Blade Runner" when he competed on two fibre-optic blades against able-bodied athletes at the London 2012 Olympic Games.
On February 14 last year, he shot dead 29-year-old Steenkamp through a locked bathroom door at his upmarket Pretoria home in a case that generated worldwide interest.
He denies the charge of murder and says he mistook Steenkamp for an intruder.
Steenkamp's parents thanked well wishers for cards, letters and other expressions of support from South Africa and across the globe.
"We understand and empathise with other parents and families who have lost a child or loved one through violence or abuse."
They also indicated that after the trial a foundation would be set up in Reeva's name.
"Reeva, who held such a passion for women's abuse issues and frequently spoke out against domestic violence, intended to one day open an establishment where abused women would be cared for."
