The photos in the Sunday People were taken about a week ago outside a restaurant in Mayfair, central London.
"The pictures are horrific but give a far more drastic and violent impression of what took place," he reportedly told London's Evening Standard.
Ms Lawson has not commented. Police say they are examining the images.
Officers from the Community Safety Unit for Westminster said they were aware of the article and were making inquiries to see if further investigation is necessary. No complaint has been received.
In Monday's Evening Standard, Mr Saatchi said: "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.
"There was no grip, it was a playful tiff.
"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 and Mr Saatchi, a former advertising executive, have been married since 2003. She has two children, Cosima and Bruno, from her marriage to journalist John Diamond, who died in 2001.
Ms Lawson's spokesman confirmed that she had left the family home with her children, but did not say whether it was a permanent or temporary move.
I can not believe this guy. He actually really seems to believe that his actions were reasonable! And if he behaves like this in public, I dread to think how he is in private.