"Mark McGowan's comments yesterday were sad ... give it up, mate," Mr Littleproud told the Nine Network on Tuesday.
The deputy Nationals leader, who worked with Mr Dutton in the defeated Morrison government, came to his coalition colleague's aid after Mr McGowan delivered a scathing assessment of the former defence minister.
The premier said an "extremely conservative" Mr Dutton did not fit with modern Australia.
"I actually don't think he's that smart," he said.
But Mr Littleproud said Mr Dutton provided the balance Australians were looking for in a federal leader.
"On economic and national security he is quite hard ... (but) he is more pragmatic on some of the more social and environment issues than people think," he said.
Victorian Premier Daniel Andrews said he would "wish" Mr Dutton well if he was chosen as the opposition leader and "welcome" him to dinner in Melbourne.
"You can make your own judgments about how much of a worldview I would share with Peter Dutton and how much he'd share with me. I'm trying to be as polite as possible," Mr Andrews said.
"You guys need to remember this - it wasn't that long ago when these people were running around saying that we're all gonna get murdered by an African gang and we couldn't go out for dinner.
"This is the sort of low road politics that these people played just a few years ago. And if any of you think they've changed, well think again."
Meanwhile, Acting Prime Minister Richard Marles believes Mr McGowan always has "wise things to say".
"I think the point here is ... what we saw from the Liberals was an attempt to create division where it didn't exist, and that diminished the national interest," he told Sky News.
The Liberals need a new leader after defeated prime minister Scott Morrison resigned following the weekend's election loss to Labor.
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