Barnaby Joyce has described the breakdown of his marriage as “one of the greatest failures in [his] life” but refused to answer questions about his relationship with a former staffer on the basis of privacy.

On the ABC’s flagship current affairs program 7.30, Australia’s deputy prime minister denied any wrongdoing but refused to say whether the relationship started while Vikki Campion was his media adviser.

Joyce’s relationship was made public by the Sydney Daily Telegraph on Wednesday with a front page photo of Campion visibly pregnant.

The revelation provoked an outraged response from Joyce’s wife, Natalie Joyce, who said in a statement that it was “devastating on many fronts” and that she felt “deceived and hurt”.

While the opposition Labor and Greens parties chose not to attack Joyce, citing privacy issues and concern for Campion, debate swirled about whether the Nationals leader’s public opposition to marriage equality on the grounds of traditional values made the story a matter of legitimate public interest.

“Private matters remain private,” Joyce told ABC’s 7.30. “I can’t quite fathom why basically a pregnant lady walking across the road deserves a front page. I don’t know what the political purpose is to that.”

Joyce said there were “no problems” such as public expenses incurred to conduct the relationship because “we have made sure that private matters remain private and anything on a public account has been to do with my work as a politician”.

He denied any element of coercion or power imbalance stemming from his position as Campion’s boss, saying “there’s nothing beyond the consensual”.

Joyce acknowledged the breakdown of his marriage was “incredibly painful for everybody involved”.

“I failed, and I’m obviously incredibly sorry about that, but I’m also – like other people – incredibly hurt that private issues get dragged into the public arena.”

Joyce shot to fame internationally in 2015, when he threatened to have dogs belonging to the actors Jonny Depp and Amber Heard put to death for breaching biosecurity rules. He later suggested that the Australian government could investigate whether Depp committed “perjury” by smuggling his dogs, Pistol and Boo, into the country while knowing it was illegal.

In October the high court ruled Joyce was ineligible to sit in parliament because he was a dual New Zealand citizen, one of nine politicians thus far to resign or be forced out by a rigid but until recently little-enforced constitutional disqualification.

After a campaign in which he was forced to fend off questions about his private life, Joyce won back his seat of New England in a resounding victory and resumed his position as Nationals leader and deputy prime minister to Liberal leader, Malcolm Turnbull.

Campion, a former journalist, left Barnaby Joyce’s office in April to work for one of his close Nationals colleagues, the resources and northern Australia minister Matt Canavan.

Joyce has noted she is no longer employed by the Turnbull government because her contract ended during the December reshuffle.