Malcolm Turnbull has doubled down on support for the marriage equality plebiscite, staring down a push from a group of business chief executives calling for the social reform to be passed.

The chief of the Business Council of Australia, Jennifer Westacott, one of the more than 30 high-profile executives who penned the letter to the prime minister, has stood by the call after a spray from the immigration minister, Peter Dutton, about the “fringe” issue.

“That’s his opinion – we’re all entitled to our views,” Westacott told ABC radio on Friday, insisting no one has been arguing harder for other issues such as tax reform than her.

Heads of some of the country’s largest companies penned a letter to Turnbull as part of Australian Marriage Equality’s equality campaign urging him to legislate for same-sex marriage. They included the heads of ANZ, Commonwealth Bank, Holden, Qantas, MYOB, Football Federation Australia and the National Rugby League.

Asked about the letter on Friday, Turnbull told 3AW Radio in Melbourne the chief executives “should be talking to Bill Shorten and saying to him, why have you gone back on your word”, referring to Shorten saying three years ago he could accept a plebiscite.

“If we’d had the plebiscite ... it would have been passed, and gay couples would be getting married now.

“We have a commitment on a plebiscite, which we took to the election – that’s our policy. The way to ensure gay marriage is allowed is to have a plebiscite.”

In the letter, signed by 34 business and community leaders, they tell Turnbull marriage equality is good for business, employees, customers and Australia.

“In the globally competitive marketplace, customers are becoming more discerning and are selecting products and services from companies that better represent their values. By supporting marriage equality, businesses send a powerful message to their customers that they think fairness, equality and dignity should be available to all Australians … Enabling loving, committed couples to be married, regardless of their sexual orientation will contribute to a stronger economy and a more inclusive Australia.”

Dutton urged company chief executives to stop shoving “your politically correct views down our throats” and instead focus on running their businesses. He labelled their lobbying effort “bizarre” and “an outrage”.

“The CEOs would be better off out there arguing at the moment for the economy to be run a particular way or for tax to be reformed in this way so that they can grow their businesses and grow jobs, as opposed to taking on these moral causes,” he told Ray Hadley on 2GB radio on Thursday.

Dutton insisted the CEOs ought to leave debate on social issues to politicians, talkback hosts and “normal” people. “I just think it’s high time these people pulled back from these moralistic stances and we’d be a better society without them,” he said.

Dutton took aim at Telstra, whose CEO Andrew Penn signed the letter. Dutton said Telstra would be better off cleaning up call centre operations than wading into political debate.

“Once all that’s done, you’ve then got time on your hands to concentrate on these other fringe issues,” he said.

Marriage equality campaigner Ivan Hinton-Teoh said the minister was simply trying to shut down views he disagreed with.

“All Australians should be free to voice their views and lobby politicians, including those business leaders who support marriage equality,” he said.

“Many CEOs recognise the importance of equality for their employees and customers, and have a right to represent that to lawmakers.”