Oscar Pistorius was arrested at his Pretoria home on Thursday after his girlfriend was shot and killed at his house.
The Olympic and Paralympic athlete was charged on Friday with the murder of 29-year-old Steenkamp, who was shot dead at his luxury Pretoria home.
He was contracted to compete in races in Australia, Brazil, Britain and the United States between March and May.
"I have decided that following these tragic events that we have no option but to cancel all future races that Oscar Pistorius had been contracted to compete in to allow Oscar to concentrate on the upcoming legal proceedings," Pistorius's manager Peet van Zyl said on Sunday.
Sponsors and partners would in the meantime maintain their contractual commitments awaiting the outcome of the legal process, said Van Zyl.
Pistorius is accused of killing his girlfriend. His bail hearing on Tuesday will take place on the same day a private funeral is due to be held for Steenkamp. He faces a life sentence if convicted of premeditated murder and remains in custody in Pretoria ahead of that hearing.
The City Press on Sunday reported that police found a bloodied cricket bat at his house.
'Lots of blood'
"There was lots of blood on the bat," one source told the paper.
Police are probing whether the bat was used to assault Steenkamp, who was shot four times, including in the head, during the early hours of Thursday, or if she may have used it to defend herself, the newspaper said.
"The suspicion is that the first shot, in the bedroom, hit her in the hip. She then ran and hid herself in the toilet … He fired three more shots," the police source told City Press.
On Sunday police spokesperson Neville Malila refused to comment on the reports of the cricket bat.
"I don't know where they got it from, but they didn't get it from any official source in the police," said Malila.
The newspaper described the case against Pistorius as "rock-solid".
'Numb with shock'
Pistorius's family denied he intentionally killed the blonde cover girl. His 89-year-old grandmother, Gertie Pistorius, told Agence France-Presse (AFP) the killing was accidental.
The family has said the 26-year-old, who is widely seen as an adrenaline junkie with a love for speed and guns, is "numb with shock as well as grief" over Steenkamp's death.
"I know it was a mistake anybody can make," Gertie told AFP. "I have got my trust in my [grandson] and I have got my trust in the case, and I am sure things will go the right way" she said.
Authorities rejected suggestions that Pistorius mistook Steenkamp for an intruder.
His father, Henke Pistorius (59), was quoted by Britain's Sunday Telegraph as saying the family had "zero doubt" his son shot Steenkamp on instinct after mistaking her for an intruder.
"When you are a sportsman, you act even more on instinct," he said. "It's instinct – things happen and that's what you do."
When contacted by AFP, the father denied speaking to the Sunday Telegraph and refused to provide any further details. The newspaper's reporter Aislinn Laing confirmed she had spoken to the father on Saturday.
'I've killed my baba'
Police said there had been several previous domestic incidents at Pistorius's home. Other reports suggested there had been an altercation between the two lovers that had spilled over from Wednesday night, when neighbours called security guards complaining about a "commotion" inside Pistorius's home.
Britain's Sunday People said a sobbing Pistorius had phoned his friend, Justin Divaris, at around 4am (2am GMT) on Thursday telling him: "My baba [baby], I've killed my baba. God take me away."
Pistorius was a national icon who inspired people around the world when he became the first double amputee to compete against able-bodied athletes in the Olympic Games last year.
Meanwhile, the family of Steenkamp said on Sunday her body was back in her hometown of Port Elizabeth and a private funeral will be held on Tuesday.
The family said that the model will be cremated in a ceremony closed to the public and the media in the city.
Pistorius was charged with her murder and is expected to make a second court appearance on Tuesday for the start of his bail hearing.
Tribute
The 29-year-old Steenkamp was seen laughing and smiling on television on Saturday night after the South African Broadcasting Corporation chose to air the first episode of reality TV show Tropika Island of Treasure 5, in which she was featured.
Her family said it did not oppose the programme being aired because Steenkamp wanted people to see it and a short tribute to her was shown before the episode.
A fellow contestant on the show told AP Television News that Steenkamp "was always making sure everyone was OK".
"Fun, crazy, loving, beautiful, gorgeous. She really was an angel and I still haven't come to terms with what happened," Katleho Molai said of Steenkamp. "I haven't really eaten, I'm struggling to sleep. So it's been really hard to come to terms with what's happened to her."
Pistorius has built up a powerful team of lawyers, medical specialists and public relations experts for his defence.
Stuart Higgins, a former editor of UK tabloid the Sun, whose lengthy list of clients includes British Airways, Chelsea FC and Manchester United football club, will be handling public relations in the case.
One of the lawyers, Kenny Oldwage, acted for the driver in a 2010 accident that killed former president and anti-apartheid icon Nelson Mandela's great-grandchild Zenani. The driver was acquitted. – AFP, Sapa-AP