Mr. Joyce, 50, has denied groping and other ministerial misconduct. He has spent much of the week offering defiance and remorse, and trying to hold on to his job.

He acknowledged his relationship with Ms. Campion on Tuesday, apologizing to his family, his constituents and the National Party of Australia, which he still leads.

But he also told his party colleagues he would not step down. “Every political career has a time of trial,” he said.

His stand fits with his longstanding “just a bloke” appeal. He grew up on a farm in Tamworth, in Australia’s southeast, which is home of the nation’s largest country music festival. Mr. Joyce is known as an off-the-cuff maverick who is loyal less to ideology than to his constituents.

But since 2004, he has been a Canberra man. He was a senator for Queensland and then joined the House of Representatives in 2013. He became leader of the National Party and deputy prime minister in 2016.

Mr. Joyce is no stranger to scandal. A few years ago he made headlines worldwide when he threatened to euthanize two dogs belonging to Johnny Depp and Amber Heard after the celebrity couple brought them to Australia without the proper documentation and quarantine.

Last year, Mr. Joyce was one of several politicians revealed as holding dual citizenship.

After the High Court ruled that he had been ineligible to run for Parliament because of it, Mr. Joyce renounced his New Zealand citizenship and returned to his district to campaign again for his seat. He won comfortably.