"I'm getting the sense that voters are a bit sick of the story that it's nearly looking like a campaign to unseat Barnaby", he said.
Joyce was re-elected in a by-election for his constituency seat after stepping down and renouncing his citizenship of New Zealand.
Overnight Australian time, the Prime Minister held several high-profile meetings, including with the head of the US Treasury Steven Mnuchin and the chair of the Federal Reserve Jerome Powell.
Turnbull was accused of making "a shocking error of judgment" with Joyce who has four daughters.
Mr Turnbull did not address the formal complaint against Mr Joyce at a press conference in Washington DC early this morning.
But he opted to take leave.
Mr Joyce has faced a litany of scandalous media headlines in the past fortnight, after the revelation his former media advisor Vikki Campion is expecting his child in April, and the couple was living rent-free in the apartment of a National party donor.
The National Party will want Barnaby Joyce back in some leadership capacity in roughly 12 months.
But Joyce's leadership has continued to be dogged with questions of potential breaches and conflicts of interest. "I've asked for the right of the person who's made the allegation and I've asked for my right of defence that that be referred to the police".More news: Florida shooting survivor: Trump Jr. is 'immature, rude, and inhuman'
Depp later referred to Joyce as looking like he was "inbred with a tomato".
The Nationals MP said he hoped to provide a "circuit breaker" for his pregnant partner, and estranged wife. "It's not fair on them".
Joyce said the media attention was completely and utterly unwarranted. Joyce has denied the allegations made in the complaint. "I don't believe any of them have been sustained", he said.
Greens leader Richard di Natale says Joyce's selfishness meant the issue dragged on a week longer than required. "The issues are related to Barnaby".
Barnaby Joyce has capitulated to intense pressure and announced he will stand down, declaring the government needs clear air and he could not continue on the frontbench with an allegation of sexual harassment hanging over him.
"He also told the media, "(It has been an) incredible privilege, that I'm so humbled by, to have been the Deputy Prime Minister of Australia".
Opposition leader Bill Shorten criticised the secret coalition agreement between the Liberals and the Nationals. As SBS notes, he will also lose his position as Infrastructure and Transport minister upon his move to the backbench.
Barnaby Joyce's imminent resignation could be even more troublesome for the PM.
With a ballot to determine the fate of the Deputy Prime Minister scheduled for 8pm on February 24, Michael McCormack, the Minister for Veterans Affairs and Defense Personnel, is already tipped to become a frontrunner.