Pistorius, who is serving a five-year prison sentence for her murder.
Jacqui Mofokeng, a member of a women's advocacy group, said Thursday that Steenkamp's mother June told her it was the "best day ever for Reeva" when news broke that Pistorius would not be released as expected on Friday after just 10 months behind bars.
Justice Minister Michael Masutha said Wednesday a parole board decision taken in June to free Pistorius and allow him to serve out the rest of his sentence under house arrest was "premature" and had been suspended pending review.
The review panel has up to four months to make its decision.
Mofokeng told reporters she had exchanged text messages with June Steenkamp on Wednesday about the minister's decision, which came as the family was marking what would have been Reeva's 32nd birthday.
Steenkamp family lawyer Tania Koen also said Reeva's parents welcomed the minister's decision, adding that they "have always had faith in the justice system".
- 'Insult' to women -
Reeva Steenkamp, a law graduate and model, was shot dead by Pistorius in the early hours of Valentine's Day in 2013.
The athlete, now 28, admitted during a nine-week trial watched around the world that he killed her but claimed he mistook her for an intruder.
Pistorius was convicted of culpable homicide in October and sentenced to five years in prison with a possibility of house arrest after serving one sixth of his sentence -- a regular occurrence under South African law.
The prosecution has appealed the verdict and is seeking a murder conviction, saying Pistorius deliberately killed Steenkamp after an argument.
Mofokeng said the news Pistorius would stay behind bars had "changed the mood entirely" of the emotional birthday beach gathering for Reeva held near the Steenkamp home town of Port Elizabeth on Wednesday.
"They said it was a better birthday than last year," said Mofokeng, who also serves as spokeswoman for a provincial branch of the ruling African National Congress.
Masutha's decision followed a petition launched by the PWMSA which said that allowing Pistorius to be freed after only 10 months in prison and during women's month was an "insult" to women.The minister has asked the parole board to review the case, kicking off a process that may take several months and almost guarantees the sprinter will remain behind bars.
The parole review board which includes three judges "has four months" to evaluate and finalise the case, said justice ministry spokesman Mthunzi Mhaga.
The review panel will look at whether the parole process was properly followed and the law applied correctly, said Mmule Motsamai Madisa, regional head of Correctional Services.
"The offender remains behind bars until the review process is concluded," he said.- 'Blessing in disguise' -
"It was a blessing in disguise that the minister, through us, could see the loopholes," said Mofokeng.
"Oscar will still have his day in court," she said, referring to the prosecution's appeal "we are hoping and wishing him to get between 10 and 15 years, no parole."
The Steenkamps have said in the past that 10 months behind bars is "too short" a time for Pistorius to pay for killing their daughter.
"They have always had faith in the justice system," said lawyer Koen. "They have always believed in the justice system and this process proves to them that the system does work and maybe they will see justice for Reeva."Koen said that the Steenkamps still plan on meeting Pistorius face-to-face as part of their healing process.
"They do want to see him," said Koen.
Lawyers representing Pistorius have not indicated if they intend opposing the justice minister’s decision.
"No decisions have been taken, and the family will take their time to calmly consider the way forward," said Pistorius family spokeswoman Anneliese Burgess.
But either way, the Pistorius defence team will head to the supreme court in November to fight the state's appeal of the runner's sentence.
Should the appeal court find Pistorius guilty of the more serious charge of murder, he could be sentenced to a minimum of 15 years in jail.