Ontlametse was one of the two South African young women living with Progeria, an extremely rare genetic disorder of rapid ageing at a very early age.
Doctors did not think Ontlemetse would live to see her 14th birthday, but last month she turned 18 after having finished matric.
She died at George Mukhari Academic Hospital in Ga-Rankuwa, Pretoria, on Tuesday after experiencing breathing difficulties.
She was from Hebron, outside Mabopane in Tshwane. Ontlametse paid a courtesy call on Zuma on the eve of her 18th birthday last month where he presented her with a birthday cake as well as a bouquet of flowers.
In a statement on Wednesday, Zuma said he had been touched by meeting Ontlametse, and said he was impressed by her zeal in life.
"Our lives were most touched by meeting Ontlametse last month. She was very special indeed. I was impressed by her sharp intellect, warm personality, brilliant ideas and her determination to use her condition to motivate others that they can achieve their goals regardless of any challenges," Zuma said.
"A brave young fighter has fallen. May her spirit inspire all others living with disabilities or facing any difficulty, to soldier on as she did and live life to the fullest. We are really proud of her. We wish to convey our utmost condolences to her mother, her whole family and the Ontlametse Phalatse Trust for this sad loss. May her soul rest in eternal peace."
Ontlametse's goal was to be a life coach and motivational speaker.
Zuma, who turns 75 on Wednesday, had also invited Ontlametse and her mother, Bellone Phalatse, with whom he shares his birthday, to join him in his birthday celebration.
Zuma committed to build Ontlametse's family a home and provide her with transport for her special needs as well as improved medical care.
He committed the Jacob G Zuma Foundation to working with her Ontlametse Phalatse Trust to assist her, and that he would also speak to relevant government departments as she is a "special child of South Africa".
"The President remains committed to fulfilling his undertaking to help the family with a house according to Ontlametse's wishes," the Presidency said.
Ontlametse's funeral arrangements would be communicated during the course of the week.