Over the weekend, the Culture Secretary shared a doctored image on Twitter that portrayed Mr Johnson as Julius Caesar, with Mr Sunak as Brutus wielding a knife behind his back.
A string of Conservative MPs quickly condemned Ms Dorries and branded the attacks on the former chancellor as “dangerous” in the wake of the murder of Sir David Amess.
Speaking to Times Radio this morning, the Work and Pensions Secretary, who is Ms Truss’s campaign manager, distanced the Foreign Secretary from Ms Dorries’ retweet.
Ms Coffey said: “Well, I wouldn’t have done it. The Liz for Leader campaign certainly didn’t do it. Nadine chose to do it. I’ve made her aware that many colleagues were upset by it.
“It’s for Nadine to decide how she runs her social media. But all I say is that I’m really here to focus on Liz rather than other news.”
She added: “I’m not going to go into individual conversations, but she recognised that other people would have been upset by some of this, but she’s very keen to make the case herself.
“And Nadine is a very special lady. She was full of life yesterday in her role as Culture Secretary, supporting the lionesses, too. But I’m really here to talk about Liz Truss.”
It’s not even a year since the stabbing of Sir David Amess at his Southend constituency surgery, so I think this is very, very bad taste, dangerous even
The former chancellor was asked about accusations he is a “backstabber” on the BBC Radio 4 Today programme, but said he would not comment specifically on “what others are choosing to say”.
He added: “I will tackle the broader claim that they (the accusations) relate to, because I do think there is a risk that people are looking at the last few months of the Government with slightly rose-tinted glasses about what it was really like.
“Because it wasn’t working as it should, and crucially the Government found itself on the wrong side of a very serious ethical issue, and, for me, also going down the wrong economic path, and that’s why in the end more than 60 MPs at the last count, I think, resigned from the Government, of which I, after a lot of deliberation and months of standing by the PM, was one of them.”
Writing in the Mail on Sunday, Ms Dorries accused the former chancellor of “planning a coup for a very long time” and said she commented on his dress sense to “alert Tory members not to be taken in by appearances in the way that happened to many of us who served with the chancellor in Cabinet”.
The Culture Secretary had previously criticised the Tory leadership hopeful for wearing Prada shoes, arguing that such a display of his wealth shows he is out of touch.
Business minister Greg Hands described Ms Dorries’ actions as “distasteful” and “dangerous”, telling Sky News: “I’m sure Liz Truss would disown this kind of behaviour.
“I think this is appalling. Look, it’s not even a year since the stabbing of Sir David Amess at his Southend constituency surgery, so I think this is very, very bad taste, dangerous even”.
Mr Hands, who is backing Mr Sunak in the race for No 10, added: “I do find it distasteful.”
Welsh Secretary Sir Robert Buckland, another supporter of Mr Sunak, also criticised the behaviour.
“I think that sort of imagery and narrative is not just incendiary, it’s wrong,” he told BBC Radio Wales.
“I think it’s time for those who think that an argument about Prada shoes or earrings is more important, for instance, should wind their neck in and let people talk about the issues rather than the personality”.
Former Northern Ireland secretary Brandon Lewis, who has thrown his weight behind Ms Truss in the leadership contest, told Sky News: “It’s certainly not the sort of thing I would tweet.”
He added: “Nadine is well-known as having strong views on things. Nadine speaks for herself, she’s very much an individual on that. But that is not a position that Liz would take”.