Andrew Bailey said that there are some things that should only be said when the Chancellor is announcing a Budget.
Mr Bailey was being quizzed by MPs, including over the promises made by Mr Zahawi to cut income tax by 2p over the next two years.
He declined to answer several questions that touched on the election of the next Conservative Party leader.
Normally financial policy and fiscal policy, which you have to take account of, is done in Budgets, not in Tory leadership elections by an existing chancellor
Angela Eagle, Labour
But Labour’s Angela Eagle repeatedly asked about Mr Zahawi’s comments in interviews.
“Normally financial policy and fiscal policy, which you have to take account of, is done in Budgets, not in Tory leadership elections by an existing chancellor,” she said.
“I care less about what the other 15 or 20 or however many there are at the moment think about this, but I do care about somebody who is actually the Chancellor who is running around doing it.
“That can move markets, can’t it? That can cause problems.”
In response, Mr Bailey said: “I don’t like offering views on the constitution, but I don’t think things that should be done in Budgets can ultimately be done outside Budgets but, obviously, all of you have all sorts of views on these matters.”
Mr Zahawi is one of many candidates vying to cut taxes if they become the next prime minister.
Others, including Attorney General Suella Braverman, Foreign Secretary Liz Truss and former foreign and health secretary Jeremy Hunt, have also promised to reduce taxes.
Former minister Robert Jenrick, who is backing Rishi Sunak for the top job, on Monday criticised the candidates for “announcing fantasy tax cuts to help get through a leadership election, I think, is unwise”.