The Paralympian and Olympian, according to reports in Afrikaans-language newspaper Beeld on Saturday, carried the 29-year-old down the stairs and tried to resuscitate her.
Security guards who heard the shots also reported spatters of blood along the route Pistorius walked with her as he sought help.
The paper claimed further that Steenkamp was shot while sitting in the bathroom, with forensic teams examining the bathroom door, which was struck by bullets.
Prosecutors charged the man famous to many as the ‘Blade Runner’ with pre-meditated murder. If found guilty, the 26-year-old would face at least 25 years in prison.
Pistorius denies the charge, and in a statement released by his agent he said that he would dispute it "in the strongest possible terms".
The claims in Beeld have not been confirmed by police, with spokesman Lieutenant Colonel Katlego Mogale saying only that the claims were part of the ongoing police investigation.
Pistorius will remain in a police cell until Tuesday at least, when another hearing takes place to establish whether he can be granted bail ahead of a full trial.
Meanwhile Pistorius’s family and friends have come to his defence in statements.
Henke Pistorius, Oscar’s father (pictured above), told the Daily Telegraph: "We just want this over with. Until it's proven otherwise, I can't believe that this was anything but a tragic accident."
Uncle Arnold Pistorius added in a statement that his nephew and Steenkamp had been happy and were thinking of the future.
"They had plans together and Oscar was happier in his private life than he had been for a long time," he said.
"We are in a state of total shock - firstly about the tragic death of Reeva who we had all got to know well and care for deeply over the last few months.
"All of us saw at first hand how close she had become to Oscar during that time and how happy they were."
The suggestion that Pistorius's family was close to Steenkamp runs counter to comments from Henke Pistorius, who told the New York Times he had never met his son's partner.
"I don't discuss my son's relationships. I have, in fact, not met the lady," he was quoted as saying.
Arnold Pistorius reiterated the family's belief that the track star - a double amputee who became one of the biggest names in world athletics when he ran at last year's Olympics - had not shot Steenkamp deliberately.
"After consulting with legal representatives we deeply regret the allegation of premeditated murder," Arnold said.
"We have no doubt there is no substance to the allegation and that the state's own case, including its own forensic evidence, strongly refutes any possibility of a premeditated murder or indeed any murder at all."
Annie Kruger, Pistorius’s cousin, was quoted by Beeld as saying: “We are all very sad for him, the whole thing is terribly bad for him. We want the right things to happen (with reference to the legal process), but it feels like people are judging a little too hastily."
Steenkamp’s body is to be flown to Port Elizabeth ahead of a memorial service on Tuesday, reports in the South African press said.
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