The husband of Nigella Lawson has said the incident caught on camera was a playful tiff, as the TV chef and her children are seen leaving the family home.
Mr Saatchi, the millionaire art dealer, leant over and appeared to grasp the television cook’s neck as they sat at an outdoor table at Scott's in Mayfair, central London, where they had been celebrating his 70th birthday.
However in a statement today, the 70 year old millionaire art dealer told the Evening Standard newspaper: "About a week ago, we were sitting outside a restaurant having an intense debate about the children, and I held Nigella’s neck repeatedly while attempting to emphasise my point."
He maintains the couple had made up when they got back to their home.
“There was no grip, it was a playful tiff. The pictures are horrific but give a far more drastic and violent impression of what took place. Nigella’s tears were because we both hate arguing, not because she had been hurt."
However Nigella, was seen driving away from the marital home in Chelsea, west London, yesterday in a taxi with her son, who carried a large suitcase.
Asked to comment on reports that the popular celebrity cook had moved out, her spokesman said today: “I can clarify that she has left the family home with her children.”
Scotland Yard said its officers were aware of the pictures but stressed that it had not received a formal complaint from either Ms Lawson or any member of the public.
A spokesman added: “Inquiries are in hand to establish the facts in order to assess whether an investigation is necessary.”
Mr Saatchi also pinched his wife's nose during the argument on Sunday June 9. Ms Lawson was said to have had "a real look of fear on her face" and left the restaurant in tears.
A witness described the incident as "utterly shocking".
"I have no doubt she was scared," the onlooker told The Sunday People. "It was horrific, really. She was very tearful and was constantly dabbing her eyes. Nigella was very, very upset."
The photographs prompted a storm on the Twitter website, with many condemning Mr Saatchi and expressing concern for his wife.
Ms Lawson has previously admitted that she and her husband have fiery rows, and has described him as "an exploder".
She said in 2007: "I'll go quiet when he explodes, and then I am a nest of horrible festeringness."
The row occurred shortly after the couple had finished eating at Scott's, a seafood restaurant which is a popular haunt for celebrities.
They were at their favourite table, which is outside because Mr Saatchi is a smoker. It is partly sheltered by olive trees but the incident could be clearly seen and heard by other customers and those passing on the street.
As Mr Saatchi tapped his cigarettes on the table, Ms Lawson was said to have downed a glass of red wine before speaking in a trembling voice. She placed a hand on his left wrist on the table and, at one point, she leant over and kissed his cheek.
The witness said: "She raised her voice and got angry but at the same time was trying to calm him down, almost like you would try to calm down a child. The kiss was a strange thing. He was being intimidating, threatening."
The couple are due to celebrate their 10th anniversary in September. Ms Lawson's first husband, John Diamond, died of throat cancer in 2001 aged 47.
Neither would comment yesterday as they left their home separately. Ms Lawson got into the taxi with her son Bruno, from her first marriage, who carried a large black suitcase.
It was not the first time that they have argued in public. Mr Saatchi, co–founder of the Saatchi & Saatchi advertising agency who has an estimated fortune of £100million, was pictured pressing his hand over his wife's mouth as they dined at Scott's last year.
Ms Lawson, the daughter of the former chancellor Nigel Lawson, now Lord Lawson of Blaby, has previously spoken about how she was physically abused by her mother as a child, describing how she never felt she could please her.
She said her complicated childhood meant she was "driven by fear" and had developed a relentless need to please people.