With Foreign Minister Julie Bishop also out of the country, the role has been assumed by Senate leader Mathias Cormann, who said ahead of Joyce's decision that any harassment claim must be taken seriously.
The Nationals President Larry Anthony said the party had greeted the news of Joyce's resignation with "a heavy heart", The Guardian reported. "I never tried to be anything else".
While leading a major delegation to the United States, Mr Turnbull was asked twice about whether he still supported Mr Joyce and told reporters it was not up to him.
Mr Joyce described his leader's remarks as "inept" and "completely unnecessary".
"I recognise Mr Joyce for his service to the party over many years and acknowledge his work dedicated to the people of regional Australia".
Mr Joyce famously threatened to have the fugitive pooches put down. "I don't believe any of them have been sustained", Joyce said.
Mr O'Brien told ABC's 7.30 Report, in his experience people wanted Mr Joyce to stay.
Both of the region's MPs also backed controversial legislation introduced by the Prime Minister which banned sexual relations with staff.
Joyce, who has been on personal leave this week with his new partner and former staffer Vikki Campion, will officially quit as Nationals leader on Monday and go to the back bench.
"It's 100 years since Sir John Monash led Australian and American troops into battle, and ever since then Australians and Americans have fought side by side to defend our freedoms, to defend our shared values", Mr Turnbull said.
Joyce revealed in December he had split from his wife in a statement to the Australian Parliament.
Mr Turnbull accused his deputy of making a "shocking error of judgment" by having an office affair. "I'll have other things on my mind", he said.
The issue has dominated headlines in Australian media this month, taking the spotlight away from the prime minister's policy agenda, including his bid to legislate corporate and personal tax cuts.
WA Nationals leader Mia Davies says Barnaby Joyce has lost the support of the party in Western Australia because of the "ongoing damage" he is causing the party.
Mr Joyce will formally resign on Monday when parliament resumes and there will be a ballot for his position.
Australia's deputy prime minister Barnaby Joyce has finally resigned, after a series of sex scandals that have plagued the Australian government and dominated the news agenda for weeks.
Opposition leader Bill Shorten criticised the secret coalition agreement between the Liberals and the Nationals.
An avalanche of unfavourable yarns about the New England MP have made things very tough for him the past few days, so he chose to hang up his Deputy Prime Minister hat (but not his trusty Akubra, obviously).