Mr Joyce will remain in Parliament as a backbencher.
"As he said, he believes he can not do that from the despatch box", Mr Turnbull said, referring to the box used by frontbenchers speaking in Federal Parliament.
Mr Joyce has told other media outlets he was seeking legal advice.
The saga has raised questions about the unity of the coalition headed by Mr Turnbull, who is leader of the Liberal Party. He is expecting a child with his former media secretary.
Mr Pitt said his priority was working for his constituents "on announcements and policy, like the cashless debit card, which I've been working tirelessly on to help the vulnerable children in our community".
Barnaby Joyce has finally caved under pressure and sensationally stepped down as leader of the Nationals and as Deputy Prime Minister. Moving back to the bench, he will continue to be a part of the parliament.
Earlier today there were reports that a formal sexual harassment complaint had been made against Mr Joyce.
Things have been tense with the PM too.Malcolm Turnbull held a tense presser last week where he slammed Barnaby's bad decisions and poor judgement, and announced a ban preventing ministers from having sex with staffers as a result of Joyce's actions.
The outgoing deputy prime minister said he had only given notice of his resignation to Senator Mathias Cormann, who is filling in as acting prime minister while Turnbull is on a visit to the US.
Joyce's travails deepened when Broad told the ABC on Thursday he had the endorsement of his local branch in the Mallee to call on Joyce to resign the leadership of the National party next Monday.
The move to the backbench means he will give up the portfolios of Infrastructure and Transport and his salary will drop from $416,000 to about $200,000 a year. "The stand-off it invoked between the cabinet's two most senior figures now represents the gravest threat to the Coalition government since it was formed", the Herald editorial said.
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