Hillary, 28, had disappeared on Friday and the EFF had called on communities for help in finding her.
The party confirmed on Tuesday that she was found dead.
Minister of Arts and Culture Nathi Mthethwa paid tribute to Hillary saying her death was tragic.
ANC national spokesperson Pule Mabe said they were saddened by the news of Hillary’s the death and called on law enforcement agencies to act swiftly in investigating and prosecuting the matter.
“The painful circumstances of her death paints a disturbing picture of violence which is deeply embedded in our communities especially against women and children.
“The ANC will continue to rally society against acts of gender-based violence whenever they occur. We call on the SAPS to fulfil its mandate rapidly and investigate the circumstances around this tragic moment in the Gardee family, to enable an effective and efficient prosecution by the NPA, said Mabe.
Pemmy Majodina, the ANC’s chief whip in Parliament, said they felt the pain for the Gardee family lost their daughter.
She called on law enforcement agencies to find those responsible for this crime and bring them to book.
Majodina said they wanted the authorities to act against those behind her murder.
“Losing a child is the most heart-breaking tragedy a parent can go through and leaves a void that cannot be filled. No parent deserves to go through what the family is going through at this point, to see their child’s life ended abruptly in the prime of her youth. To the three-year -old who will be left without a mother, the pain is unbearable to contemplate,” said Majodina.
“To the Gardee family, friends and relatives, the ANC Caucus extends its heartfelt condolences on the tragic passing of Hillary at a time when our country is fighting the scourge of gender–based violence. We call on anyone with any information that may lead to the arrest of the perpetrator/s of this dastardly barbaric act to report such information to the police,” she said.
The DA also paid tribute to Hillary. The party’s deputy chief whip Siviwe Gwarube said losing a child was tragic and they were also mourning the loss of Hillary.
Gwarube said the scourge of gender-based violence continued in the country.
She said Hillary's killing was a loss to her family and the community.
“Our deepest condolences are extended to the Gardee family on the tragic loss of their daughter. We can never consider ourselves free until the war against women is defeated,” said Gwarube.
UDM leader Bantu Holomisa also paid tribute to Hillary, saying her murder “was barbaric”.
“My condolences to her family and friends. May her soul rest in peace. This barbaric behaviour continues in this country,” said Holomisa.
IFP chief whip Narend Singh also paid tribute to the Gardee saying the death of their daughter was tragic.
“Let me on behalf of the IFP offer our sincere condolences to the Gardee family on this very tragic and sad loss,” said Singh.