"I thought that was completely unnecessary and all that is going to do is basically pull the scab off to everybody to have a look at," he said.
"Comments by the Prime Minister yesterday at his press conference, with regards to that, I have to say that, in many instances, they were inept and caused further harm."
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"I believe they were in many instances... unnecessary. The reason I say that is it was public knowledge what was being repeated, it ran on the front pages of papers and all it does is reinvest in hurt of other people.
Mr Joyce refused to stand down as the leader of the National party, saying he wouldn't quit his job because "that's not the decision of my colleagues... my colleagues support me."
"This was a personal issue that was dragged into the public arena, and I don't believe people should resign in any job because of personal issues.
He apologised to his estranged wife and three daughters and said the announcement of his new relationship made things "very difficult".
"I am incredibly sorry for the hurt I have caused Natalie, my daughters, and Vikki, since my marriage broke up last year. I say that again, I am incredibly sorry and I apologise to the people of New England and I appreciate the immense support I have received."
Earlier today the Prime Minister delivered what has been dubbed by observers as a "train wreck" press conference, where he stumbled and garbled his way through questions regarding Joyce's affair.
"It's not my job to go and investigate every rumour," Prime Minister Turnbull said.
"I can't recall when I first heard rumours but I can say to you that he did not say to me that he was having an affair with this woman. I'm not going to go any further than that.
"This is a workplace issue. It's about workplace respect. They are required to comply with the code. You know what? We are not asking very much. Ministers are well paid, they have big jobs, big responsibilities, lots of status. I'm just saying that they should not do something which we all know is wrong or inappropriate or undesirable.
"Call it what you like, it is not conducive to a good and healthy workplace."
Can the pair continue working together?
Turnbull's working relationship with deputy Barnaby Joyce is "strong", despite his public humiliation at the hand of the prime minister. Earlier cabinet minister Matthias Cormann denied Turnbull effectively told the Nationals leader to quit in the wake of his affair with a staffer, by saying he had to "consider his position".
"That is absolutely not the case," Senator Cormann told Sky News on Friday.
"I think they'll have a strong and productive and positive relationship in the future."
Turnbull on Thursday announced Joyce was taking a week's leave and would not be acting prime minister when the prime minister visits the US next week, after making "a shocking error of judgment" by having an affair with a former staffer.
Joyce this week stared down calls from within his own party to stand down, but his colleague Andrew Broad has warned it's not the end of the matter.
"I'm still waiting to see the evidence there's been an abuse of power. If I see that and it's clear, well then I'll be one of the people talking about what should be the action as a result of that," he told ABC radio. The Nationals MP, who is willing to change his support for Mr Joyce, says the party isn't going to be pushed by the media or Turnbull.
Joyce's affair with ex-staffer Vikki Campion has prompted Turnbull to rewrite the ministerial code of conduct, which covers the behaviour of senior government MPs, to include a clause banning sexual relations between ministers and their staff.
Broad says the ban sends a message that "somehow the parliament is some ... orgy", something he denied.
"What I see is very dedicated people who work in parliamentarian offices and I'd hate for them to have their reputation tarnished by this innuendo," he said.
Frontbencher Christopher Pyne believes it was "incredibly disappointing" for Turnbull to have to spell out the staff sex ban.
But he praised Turnbull for showing leadership on ministerial conduct in the wake of the Joyce affair.
Mr Pyne says a modern workplace requirement, already present in some parts of the private sector, has now been made clear.
Labor frontbencher Anthony Albanese argued common sense and said no employer should be sleeping with their staff.
But he also described the announcement an exercise in distraction by the government, adding there are still concerns Mr Joyce breached other parts of the code regarding jobs for close partners and receiving a rent-free apartment from a friend.
"The ministerial code of conduct is now in shreds. The fact is it's been ignored by Barnaby Joyce," he told the Nine Network.
Crossbench senator David Leyonhjelm is concerned Mr Turnbull's clear personal disapproval is being turned into regulation.
"To make it a rule based on disapproval, I think it's bad practice," he told 3AW, not expecting Mr Joyce to see out the scandal.
With Foreign Minister Julie Bishop currently overseas, Senator Cormann will be acting prime minister when Mr Turnbull travels to Washington next week.
On whether Mr Joyce can continue to work with the Prime Minister, he said, "I am intending to make sure that, like all relationships, that this relationship gets back onto an even keel."
— Additional reporting by Jennifer Jennings, AAP
