Mr Rees-Mogg told reporters after attending Mr Johnson’s Cabinet meeting that Ms Truss is a true Brexit backer who has “always opposed Rishi’s higher taxes”, in efforts he labelled “proper conservativism”.
Transport Secretary Grant Shapps pulled out of the leadership race as he struggled to win the required nominations before the cut-off, and announced his support for Mr Sunak.
Deputy Prime Minister Dominic Raab also hailed Mr Sunak – whose resignation helped force Mr Johnson’s downfall – as a “true Conservative” as he offered his backing.
After being welcomed to the stage by Mr Raab, the former chancellor told his official campaign launch that tax cuts are “a question of when, not if”.
But he said it is “not credible to promise lots more spending and lower taxes”, in a swipe at rivals who have proposed multibillion-pound tax cuts immediately.
Instead Mr Sunak, one of the frontrunners in the campaign for the Tory leadership, said he would only cut taxes “once we’ve gripped inflation”.
“We need a return to traditional Conservative economic values and that means honesty and responsibility, not fairytales,” he said.
Mr Sunak said he would not “demonise” Mr Johnson, who is expected to remain caretaker Prime Minister until after a successor is announced on September 5.
But he acknowledged he had “frequently” disagreed with Mr Johnson, who he insisted has a “good heart”.