The millionaire art collector admitted that photographs of the argument showing him leaning over and appearing to grab the television cook’s throat looked “horrific”.
But he told the Evening Standard that they gave a “far more drastic and violent impression” of what happened as they sat at an outdoor table at Scott's in Mayfair, central London, where they had been celebrating his 70th birthday.
Ms Lawson, 53, 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 she had moved out, her spokesman said: “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."
However, breaking his silence about the incident, Mr Saatchi today issued a statement in which he sought to play down the significance of the row.
“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 told the Evening Standard.
“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.
“We had made up by the time we were home. The paparazzi were congregated outside our house after the story broke yesterday morning, so I told Nigella to take the kids off till the dust settled.”
Ms Lawson’s spokesman declined to comment on Mr Saatchi’s statement.
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."
A spokesman for Scott's said: "The staff and management at Scott's are aware of the reports in the media and would like to make it clear that they did not see the alleged incident nor were they alerted to it at the time."
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.
They left their home separately yesterday, with Ms Lawson getting 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.
www.telegraph.co.uk/news/uknews/crime/10124976/Charles-Saatchi-says-hands-around-throat-row-with-Nigella-Lawson-was-playful-tiff.html