"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 emphasize my point," Saatchi, an art dealer and former advertising mogul, 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," he added. "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."
Lawson's spokesman said only, "Nigella and her children have moved out of the family home."
Sunday People, part of the stable of tabloids published by the Mirror Group, published the photos Sunday of Lawson and Saatchi at a restaurant.
The tabloid's website includes the caption: "Nigella Lawson attacked in public by Charles Saatchi."
Police have not received a complaint of an assault.
In a statement, London's Metropolitan Police said they are making inquiries to determine "whether an investigation is necessary."
The restaurant involved told CNN that its employees did not witness any such incident.
Lawson's Facebook page is filled with messages from fans expressing their support for her.
Lawson is known as the "queen of food porn." She has written numerous successful cookbooks and hosted TV shows.