She said there was no sign of forced entry at Pistorius's home. "The premises are fairly secure ... This is a fairly secure estate.''
Nike 'bullet' ad pulled from Pistorius site
Twitter offers glimpse into Blade Runner's life
Pistorius' girlfriend hinted at Valentine's Day surprise
"There's previously been incidents of allegations of domestic disputes at the home of the accused.''
Beukes said the police were talking to neighbours who heard disturbances earlier in the evening and around the time of the shooting.
Other reports suggested it was a Valentine's Day surprise that went tragically wrong.
"Obviously we are shocked,'' his father Henke Pistorius told AFP. "He is with the police and the matter is in the hands of the authorities.''
"Our thoughts are with the family of the woman involved in this tragedy,'' he said.
Afrikaans language newspaper Die Beeld reported on its website that the incident happened around 4am today (local time).
A police spokeswoman named as Captain Sarah Mcira reportedly confirmed to the website that Pistorius' girlfriend was shot in the head and arm.
Paramedics tried to revive her but she died at the Silver Lakes house.
Pistorius was said to be in shock as police questioned him at the scene before his arrest.
His girlfriend's body was removed from the house about 8.30am.
"We found a 9 millimetre pistol at the scene. A 26-year-old man was taken into custody," police spokesman Katlego Mogale told Reuters.
Mr Mogale said when police arrived they found paramedics trying to revive a 30-year-old woman.
"The deceased was shot four times and died on the scene. It is believed that she was the girlfriend of the accused," he said.
The dead woman was named as model Reeva Steenkamp.
Ms Steenkamp, who has appeared in FHM magazine, was first spotted with Pistorius at the South African sports awards in November last year.
Just yesterday, Miss Steenkamp spoke excitedly on Twitter about her plans for Valentine's Day, the Mailonline reported.
She said: 'What do you have up your sleeve for your love tomorrow??? #getexcited #ValentinesDay'.
Replying to a follower, she later added: 'That sounds amazing! Wow that's what it's all about! It should be a day of love for everyone :) may it be blessed!'
South African journalist Kalay Maistry told Sky News: "It is alleged that he thought his girlfriend, who'd come in to try to surprise him for Valentine's Day, was an intruder. It's alleged that he shot her in the arm and head."
"I think what this actually highlights is the level of fear ordinary South Africans have. This is a man who has gone to bed, it's an innocent surprise from a girlfriend and the moment he thinks someone is trying to break in he grabs his gun."
"This has come as a complete surprise for a man who's considered a national hero,'' Maistry said.
The Evening Standard newspaper reported that police had confirmed Pistorius had been charged with murder.
He is expected to appear in Pretoria Magistrates Court later today.
Tributes to Ms Steenkamp began appearing on Twitter soon after the news broke.
"You will be missed Reeva -your tweets made me laugh.RIP'' this is a tragic day for all South Africans, crime claims another'', said one Twitter user.
''I'm so sorry this had to happen to you! You are a beautiful angel now ... You made me smile! Until we meet again'', said another.
Pistorius has been dubbed Blade Runner for the blade-like prosthetics he wears for his double under-knee amputation.
He became the first double leg amputee to take part in the Olympics when he entered the men's 400 metre race and was a member of the men's 4 x 400 metre relay team at the 2012 London Games.
He won gold at the 2012 Paralympics in the men's 400 metre race in a Paralympics record time of 46.68 seconds and in the 4x100 relay in a world record time of 41.78 seconds.
He also won silver in the 200 metre race with a world record time of 21.30 seconds in the semifinal.
Pistorius had his legs amputated below the knee when he was 11 months old after he was born with a congenital absence of a fibula in both legs.
The track star's home is a large farm northeast of Johannesburg in the Pretoria region, which is heavily guarded.
In an interview with the Mail before London 2012 it was revealed he slept with a pistol next to his bed and kept a machine gun by a window.
Ms Steenkamp, a law graduate from Port Elizabeth, gave an interview to the Sunday Times in South Africa last week in which she described her boyfriend as "an impeccable man who always has her best interests at heart''.
The International Paralympic Committee (IPC) said: "At this time the IPC would like to offer its deepest sympathy and condolences to all families involved in this case.''
The organisation said it would not comment further on the shooting.
A spokesman said: "This is a police matter, with an investigation currently under way. Therefore, it would be inappropriate for the IPC to comment on this incident until the official police process has concluded.''
Pistorius timeline
1986 - Born with a congenital absence of a fibula in both legs which were amputated below the knee when he was 11 months old.
2004 - Won gold and bronze at the Athens Paralympics aged just 17.
2008 - IAAF ruled him ineligible to race against able-bodied athletes. Decision was reversed by the Court of Arbitration for Sport.
2008 - Failed to qualify for Beijing Olympics
2008 - Won three gold at the Beijing Paralympics in the 100m, 200m and 400m (T44)
2011 - Qualified for Athletics World Championships in Daegu, reached the semifinals in the 400m and won silver in the 4x400m relay.
2012 - Became the first double leg amputee to compete at the Olympics racing in the 400m, where he reached the semifinals, and the 4x400m relay. Chosen to carry the South African flag for the London closing ceremony.
Won two gold and a silver at the London Paralympics.
2013 - Charged with the murder of his girlfriend.
- With AFP
