Mr Tudge denies the accusations but has agreed to stand aside from his cabinet role while the prime minister’s department investigates.
Former press secretary Rachelle Miller alleged she was emotionally, and at one point physically, abused during a 2017 affair with the minister.
Mr Dutton said he wanted to see Tudge return to his role as education minister next year.
“I’ve always found Alan to be a very honourable and decent man,” Dutton told the Nine Network on Friday.
“He’s had an extramarital affair, a consensual one. He’s made a mistake. It’s cost him his marriage. There’s a lot of embarrassment on both sides.
“There are a lot of Australians who would find themselves in that position.”
Tudge has taken leave and says there is written evidence to contradict Ms Miller’s version of events.
“I have accepted responsibility for a consensual affair that should not have happened many years ago. But Ms Miller’s allegations are wrong, did not happen and are contradicted by her own written words to me,” he said in a statement on Thursday.
Miller last year made the affair public and described it as consensual.
But she now says it was more complicated than that, and that she was humiliated and scared.
She alleged the minister repeatedly chastised, bullied and belittled her.
At one point, she accused Tudge of physically kicking her from his hotel room bed until she ended up on the floor.
Prime Minister Scott Morrison announced on Thursday his department would look into the allegations.
Former public servant Vivienne Thom will head the investigation.
Miller said she would cooperate fully with the departmental investigation, but cast doubt on whether it would be truly independent or fair.
A report released by Sex Discrimination Commission Kate Jenkins this week found bullying and sexual harassment was rife in parliament.
One in three people surveyed said they had been sexually harassed and about a quarter said their harasser was a politician.
Miller said she wanted the government to listen to and acknowledge the experiences of women working in the federal parliament.
“The Liberal party doesn’t have a women problem, it has a men problem.”Jump to next article