"Adults can conduct their relationships, if it's consensual, respectful - that's their right."
Turnbull later declined to confirm or deny a claim that on learning about an affair, he had counselled Joyce to remove Campion from his office.
Turnbull also would not comment on a media report that Campion got a new job with a pay increase last April. She changed jobs again but her contract has now ended.
"This is a deeply personal matter relating to Barnaby Joyce and his family and I do not wish to add to the public discussion about it," Turnbull said.
"I'm very conscious of the hurt this has occasioned his wife Natalie and their daughters and I have nothing further to add," Turnbull said.
Independent lawmaker Cathy McGowan on Thursday invited legislators to discuss a potential motion in Parliament to "address personal relationships within the workplace".
"There is a belief the Parliament is behind expectations and corporate practice," McGowan said in a statement.
Independent lawmaker Bob Katter gave in-principle support for a ban.
"People's private lives are their private lives, but I do make the comment: Not staff. Please fellas, not staff," Katter told Sky News television.
"You're in such an enormously influential position with staff," he added.
Attorney-General Christian Porter described such a ban as a "very unwieldy law." Shadow Attorney-General Mark Dreyfus also questioned whether such a ban should be legislated.
Joyce, leader of the Nationals party, told Parliament in December that he had separated from his wife of 24 years, who is the mother of his four daughters. But he did not confirm his relationship with Campion, 33, until newspapers published photographs of her obviously pregnant on Wednesday.
Joyce, 50, said in a television interview that he had never used taxpayer-funded travel or accommodation to pursue the relationship. Several journalists who had made freedom of information requests concerning his expenses in an apparent attempt confirm the relationship but had found nothing untoward, he said.
She has not commented and Joyce declined to say how and when the relationship began. "I'm not going to once again go into all the iterations of a private relationship and there's nothing beyond the consensual. This is a private matter," Joyce told ABC.
- AP