Health minister Edward Argar made clear Mr Johnson was planning to stick with his claim that the Labour leader did not do enough to prosecute the serial sex offender when he was Director of Public Prosecutions.
Pressure has mounted on the Prime Minister to say sorry and fully withdraw the unsubstantiated allegation after Sir Keir had to be whisked into a police car for his protection when he was mobbed by angry protestors, some shouting Savile, close to Parliament on Monday afternoon.
Mr Johnson was rebuked by Commons Speaker Sir Lindsay Hoyle on Tuesday for the claim, as well as criticised for it by senior Tory, Labour and Liberal Democrat MPs and the Government’s own independent adviser on political violence and disruption, Lord Walney.
Mr Johnson threw the initial claim into a debate last Monday into the “partygate” scandal, threatening his premiership, when he alleged that when Sir Keir was DPP he “spent most of his time prosecuting journalists and failing to prosecute Jimmy Savile”.
After a backlash, Mr Johnson clarified his accusation by saying he was not accusing Sir Keir of personally being involved in decisions not to prosecute the serial sex offender.
Mr Argar told Sky News: “He has clarified that he was talking about Sir Keir in the context of his leadership role at the CPS, just as quite rightly Sir Keir holds him to account for his leadership role over the Government.
“That does not mean personal responsibility for individual decisions, but that’s the context and the Prime Minister has clarified that and I’ll be honest with you I suspect that is what you will hear from the Prime Minister.”
However, Sir Lindsay issued a warning to MPs on Tuesday after Sir Keir was targeted by protestors.
He told the Commons on Tuesday: “I made it clear last week that while the Prime Minister’s words were not disorderly they were inappropriate.
“As I said then, these sort of comments only inflame opinions and generate disregard for the House and it’s not acceptable.
“Our words have consequences and we should always be mindful of that fact.”
The Speaker added that he had asked the Metropolitan Police for a report into how Sir Keir was able to be targeted, stressing MPs should be able to arrive and leave Parliament safely.