The debate on marriage equality has been “resolved”, the resources and Northern Australian minister, Matthew Canavan, has said after Peter Dutton’s attack on chief executives supporting the still unlegislated social reform.

Canavan cited Malcolm Turnbull’s reiteration of support for the plebiscite on Friday, a further sign that a push by Liberal moderates who support a free vote on marriage equality has so far failed to convince their colleagues.

Senior moderate Liberals including Julie Bishop and Simon Birmingham have defended the CEOs right to have their say, and Birmingham rebuked Dutton on Sunday by calling for members to express their views in the party room.

This week a group of 30 chief executives signed a letter organised by Australian Marriage Equality urging Turnbull to legislate for same-sex marriage.

On Saturday Dutton singled out the Qantas chief executive, Alan Joyce, accusing him of using the company’s brand to push his personal view on equality.

On Sunday, the Daily Telegraph reported conservatives were rallying to block a push by a group of up to 12 Liberal moderates to write to Turnbull calling for reconsideration of marriage equality before the budget.

Asked about the moderates’ claim resolving the marriage issue would clear the air to talk about budget issues, Canavan told the ABC’s Insiders program on Sunday the argument was “unusual” because the government should focus on jobs, energy and childcare.

“There’s lots to do and the Coalition’s position on the marriage question is very clear: we think the Australian people deserve a say.”

He said of the plebiscite’s defeat in the Senate, “that was rejected by the parliament late last year”, and labelled the renewed push a “massive diversion”.

“[The prime minister] has been very clear in his views on the matter,” he said. “We’ve been very clear as a party. We had a very respectful debate on this matter a couple of years ago and it’s resolved as far as the Coalition is concerned.”

Canavan said he would like to see more “respect” in the debate, saying unspecified people had shown “a level of contempt for those with a different view”.

He rejected the idea in their CEOs’ letter that continuing to block a free vote would be bad for business, citing the fact that Australia’s biggest trading partners in Asia would not legislate same-sex marriage “any time soon”.

Asked about Dutton’s comments at a press conference on Sunday, Birmingham said that “throughout history business leaders have often step ahead of legislators in support of reforms to gender equity or racial equity”.

“I see no reason why business leaders won’t do the same when it comes to same-sex marriage.”

Birmingham said the government’s priority was childcare but “individual members are free to raise any topic at any time and we are more than capable of walking and chewing gum at the same time”.

“I would also prefer that everything is conducted in the partyroom, but in the end, people are free to express views, and argue their case.”

He added that “any such issues” with marriage equality would be worked out in the party room.

On Sky News on Sunday the health minister, Greg Hunt, who supports marriage equality, reiterated his support for a plebiscite.

“I disagree with those that seek to deny the Australian population a say,” he said. “I respect their views, I respect their right to their views. But it’s a slight perversity that some would say only the elite can participate in the debate ... and we can’t trust the population.”

Hopes for marriage equality were boosted in February by a consensus Senate committee report on ways to improve the government’s exposure draft same-sex marriage bill to better balance the right to equality and protections for freedom of religion.

But momentum on the issue has stalled since then, although Liberal moderates are still reserving the right to raise the issue in the party room.

The Liberal senator Dean Smith has said the prospect of a plebiscite was “dead” and has called for a free vote in this term of parliament.

On Monday his fellow Liberal moderate MP Tim Wilson told Sky News that, although the Coalition took the plebiscite policy to the election, the former prime minister Tony Abbott had also said that the 44th parliament would be the last to be bound on same-sex marriage.

“The question is going to eventually be, the conversation we’re going to need to have [is] around what ... policy is taken to the next election but I don’t think now is the time for that conversation,” he said.

On Sunday, the opposition leader, Bill Shorten, said it was a bit much for Dutton to accuse companies of bullying people over marriage equality.

“Mr Turnbull, I know, supports a vote in parliament on marriage equality but he just lacks the ticker to confront the bullies of the right wing of the Liberal party,” he told reporters in Sydney.