Liberal senator Eric Abetz has demanded SBS managing director Michael Ebeid hand over emails detailing his decision to support a corporate campaign for marriage equality.

The freedom of information request, which was rejected by SBS, became the subject of an intense exchange when Senator Abetz grilled the openly gay SBS boss at Senate estimates on Wednesday.

The controversy related to a letter to Prime Minister Malcolm Turnbull, signed by almost three dozen prominent business leaders, calling on him to legalise same-sex marriage. It sparked a fierce backlash from Coalition conservatives including Senator Abetz and Immigration Minister Peter Dutton.

Senator Abetz had requested all communications between Mr Ebeid, Mr Ebeid's office and Australian Marriage Equality, the lobby group that organised the campaign and drafted the letter.

SBS rejected the request on the grounds the emails were sent in a personal capacity, an explanation Senator Abetz dismissed as "demonstrably unsustainable".

He demanded to know whether any of the emails bore Mr Ebeid's professional SBS email signature, to which SBS corporate affairs director Clare O'Neil said she could not recall.

An exasperated Mr Ebeid defended his decision to sign the letter, saying: "Just because I'm employed by SBS doesn't mean I have a lobotomy of my personal views."

Senator Abetz argued the emails should be handed over because Mr Ebeid signed his name in his capacity as a business, industry and community leader, which he derived from his role as SBS.

Mr Ebeid told Senator Abetz he was "drawing an incredibly long bow". "We all signed [the letter] in our personal capacity. I'm not sure what the problem is here," he said.

"You needn't worry about that," Senator Abetz responded. "I'm asking the questions. I'm seeking answers."

Mr Ebeid said all SBS employees were "well and truly entitled" to use their work email accounts for a reasonable amount of personal communications.

Communications Minister Mitch Fifield agreed he would not be concerned by the occasional use of work email for personal purposes by his own staff. "I'd take a common sense approach," he said.

Mr Ebeid said it was in the interests of his employees at SBS for the company to support marriage equality because inequality caused enormous anxiety, stress and depression in the lesbian, gay, bisexual, trans and intersex community.

"When you have experienced discrimination over a prolonged period of time, it does affect your mental state," he said. "And when you come to work, you don't get to leave depression, anxiety, feelings of discrimination behind at the door.

"So it does affect employees - their productivity levels, how confident they feel at work. So you're not able to bring your whole self to work. And that's why so many CEOs ... think this is a very important issue to the bottom line."

Senator Abetz indicated he would not abandon his demand for Mr Ebeid's emails, and would appeal the FOI decision. "It will be pursued," he said.

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