Welfare Secretary Mel Stride said “the caravan has got to move on” from the ex-PM following the Privileges Committee report.
No10 said Rishi Sunak now considered the matter closed after MPs voted overwhelmingly to reprimand Mr Johnson for deliberately misleading them over lockdown gatherings.
Some 354 MPs to seven voted to strip him of the Commons pass afforded to all ex-parliamentarians.
The PM was among dozens of Tories who abstained with Downing Street blaming a diary clash.
His spokesman said: “He respects the decision the House has come to, this follows extensive work by the committee. But beyond that I don’t have anything more to add.”
After launching a series of blistering attacks on Mr Sunak, Mr Johnson is understood to want a ceasefire in hostilities.
Yesterday Mr Stride told colleagues: “I think really the caravan has got to move on from Boris Johnson, with respect.”
Mr Stride, who also abstained, told Times Radio that he totally accepts the committee’s findings, saying its members acted with “absolute integrity” and “diligence”.