Mr Turnbull on Thursday took aim at his deputy, saying he had made a shocking error of judgment by having a relationship with former staffer Vikki Campion, 33.
"They caused further harm. I believe they were in many instances inept, and most definitely in many instances unnecessary," Mr Joyce told reporters in Canberra on Friday.
"I listened to it and 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."
Mr Turnbull said Mr Joyce (50) had brought "humiliation" on his wife, daughters and now-pregnant partner, as the prime minister rewrote the ministerial code of conduct to ban ministers from having sex with staff.
"Barnaby made a shocking error of judgment in having an affair with a young woman working in his office," Mr Turnbull told reporters on Thursday.
"In doing so, he has set off a world of woe for those women and appalled all of us."
The prime minister on Friday said his deputy was considering his position, but he had not asked him to resign.
Mr Joyce said he did not believe people should resign in any job because of personal issues.
When asked how he could possibly work with the prime minister again, Mr Joyce said, "I am intending to make sure that, like all relationships, this relationship gets back onto an even keel."
He again defended his use of a rent-free townhouse for six months, which was provided to him by businessman Greg Maguire.
Mr Joyce has also been criticised for shuffling Ms Campion to other political jobs, and for his department's payments to Mr Maguire's businesses.
Mr Turnbull cannot sack Mr Joyce because he is leader of the Nationals, which this week fell into line behind their boss.
Liberal backbencher Kevin Andrews said the problem must be resolved before Mr Turnbull goes to the United States next week.
"Most Australians expect our leaders to be able to sit down on an issue like this in a man-to-man fashion and sort out whatever the differences there are there," Mr Andrews told Sky News.
Nationals MP Andrew Broad said he was waiting to see the evidence there's been an abuse of power, but he won't be pushed by the media or Mr Turnbull.
"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.
Mr Joyce's relationship with Ms Campion prompted a rewrite of 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.
Nationals MP George Christensen described the code ban as "bonkers".
Frontbencher Christopher Pyne believes it was "incredibly disappointing" for Mr Turnbull to have to spell out the staff sex ban, a modern workplace requirement that already applies in some parts of the private sector.
Labor frontbencher Anthony Albanese argued for common sense and said no employer should be sleeping with their staff, but also said there are still concerns Mr Joyce breached parts of the code regarding jobs for close partners and receiving the rent-free apartment.
With Foreign Minister and deputy Liberal leader Julie Bishop currently overseas, Senator Cormann will be acting prime minister when Mr Turnbull travels to Washington next week.
