Mr Joyce returned fire, saying Mr Turnbull's comments were "inept and most definitely in many instances unnecessary".
Mr Morrison has also defended the Prime Minister Malcolm Turnbull's scathing attack on his deputy Barnaby Joyce, agreeing he was "shocked and appalled" by Mr Joyce's behaviour.
Asked if Mr Joyce could be "rehabilitated", Mr Turnbull told journalist Liz Hayes: "He's apologised".
The revelations have damaged father-of-four Joyce's credibility as a family man and he's also facing claims he allowed Ms Campion to work in his and another ministerial office during the affair - potentially breaching the ministerial code of conduct.
Australian Prime Minister Malcolm Turnbull brushed aside suggestions of a rift in his coalition government on Sunday, saying there were "no issues" between the Liberal and National parties in the wake of a sex scandal that has swamped Deputy Prime Minister Barnaby Joyce.
Former prime minister Tony Abbott also waded into the public stoush to take a veiled swipe at Malcolm Turnbull.
"It's always very important to meet, to work through the various challenges and issues that we face, but the important thing is Barnaby and I are working closely together as we always have", Turnbull told reporters in Melbourne today.
"If a member of parliament has something to say to another member of parliament he or she should knock on the door or pick up the phone". The scandal prompted the Prime Minister to ban sexual relationships between ministers and their staff. Turnbull and Joyce met on Saturday for crisis talks in Sydney which the Prime Minister described as "frank and warm, friendly, good, constructive". "It's just got to end", he later told Fairfax media.
Joyce, 50, has faced severe criticism since he admitted last month that he was expecting a child with his former media adviser, the 33-year-old Vikki Campion.
Labor MP Pat Conroy described the entire scenario as a "soap opera". "There's a massive question to answer".
"Saying you're speaking for 25 million people is a bit presumptuous, but I certainly felt that the values I expressed and the action I took, would have the overwhelming endorsement of Australians". It was up to Mr Joyce's Nationals to decide whether he should continue as party leader, he said.
Joyce warned that any pressure on the Nationals to dump him "locks people in as they lock-in behind the leader".
"He is having a week off and then we'll have our party room meeting Monday after next and we will see", she said.
Mr McCormack has been floated by some within the National Party as a possible successor to Mr Joyce.
The government must call an election by May 2019.
"Does he care more about himself or the country?"