"The family will support Oscar as he serves out the remainder of the 5-year sentence handed down by the trial judge," spokeswoman Anneliese Burgess said Tuesday. "He will strictly adhere to the conditions set by the Parole Board and Community Corrections."
Pistorius was released from a South African prison Monday and is staying at his uncle's house.
He had been in prison since October last year, when a judge sentenced him to five years for culpable homicide in the killing of his girlfriend, Reeva Steenkamp
Pistorius shot the model and law school graduate on Valentine's Day 2013. He has said he mistook her for an intruder.
Last week a South African parole board said
it had approved his placement under house arrest and correctional supervision for four years.
South Africa's correctional services act allows convicted criminals who have served at least one-sixth of their sentence to serve the remainder under house arrest.
Burgess repeated several times on Tuesday that his sentence hadn't been shortened or reduced with his release.
The release didn't matter much to Steenkamp's family, according to their lawyer Tania Koen.
His release "doesn't make any difference to the Steenkamps; ultimately, their daughter is not coming back," Koen said. "They don't have a feeling of revenge, and they've forgiven Oscar Pistorius."
News of Steenkamp's killing stunned the nation, where Pistorius is nicknamed the "Blade Runner" because he ran on special carbon-fiber prostheses.
Despite having both legs amputated below the knee as a toddler, he excelled in sports, representing his country in the Paralympic Games and the 2012 London Olympics.
Steenkamp was found shot to death in his home, and he acknowledged firing the fatal shots through his bathroom door.
Last year, a judge found him "negligent" in Steenkamp's death
. But the judge said he did not commit murder nor did he intend to kill her.
Prosecutors are appealing the verdict, believing Pistorius, who is now 28, should be convicted of murder.
The state's appeal is set to take place next month.
Steenkamp's family is willing to meet Pistorius, their lawyer said. But not now, and only later if Pistorius initiates it.
"They will meet ... but only when the time is right," said the lawyer, Koen. "And that time is after appeal, when the legal system has taken its course."