"If they do not trust each other, they cannot be trusted to look out for the interests of Australia," he told parliament on Monday.
Mr Shorten says the government is focused on itself and not on helping the public, pointing to leaks about visa cases involving Home Affairs Minister Peter Dutton.
The Labor leader also took aim at Prime Minister Scott Morrison's recent use of the term "Muppets" when speaking of the recent bitter leadership battle.
"Those opposite by their own description have given up governing, even the prime minister calls his own people 'The Muppet Show'," he said.
"Two weeks ago wasn't the end of the civil war, it was just the opening shot and the next battle we see every day."
The prime minister shouldn't protect colleagues who've had claims of bullying made against them, Mr Shorten said as he ticked allegations of intimidation against women in the Liberal party off his list of concerns.
"The best place for the Liberal party to resolve all of these toxic poisonous issues, the best place for them to get it out of their system, is a good, long stint in opposition," he said.
Deputy Labor leader Tanya Plibersek took aim at Mr Morrison for pledging his support for Mr Turnbull in the days before he was knifed as leader.
She described Mr Morrison having his arm around the former prime minister while saying "I'm ambitious for this man".
"I'm ambitious for his job, that's what he should have said," Ms Plibersek declared in the lower house.
Government minister Christopher Pyne said he agreed changing leader was not the right thing to do, putting the blame on Labor for its changes during the Kevin Rudd and Julia Gillard era.
Mr Pyne insisted the Liberal party were not distracted by internal divisions.
"I agree with the Australian public that what they want is stability, they want a calm government in Australia that is getting on with the job," he said.
"Get your hand off it"
Environmental activists scaled the towering flagpoles outside Parliament House in Canberra, unfurling an enormous banner condemning the coal industry as Parliament returned.
Two Greenpeace protesters flew the bright yellow banner showing an image of Prime Minister Scott Morrison clutching a piece of coal alongside the words "Get Your Hand Off It".
"On Scott Morrison's first day as PM in Canberra, we let him know how we feel about his cosiness with the coal industry via a banner outside of Parliament House," the green group posted to Twitter.
Meanwhile, farmers and their supporters are holding a rally in Canberra to demand the federal government take urgent action on climate change.
A ute convoy with farm dogs made its way around State Circle on Monday morning before speakers addressed the crowd.
"Rural Australia is on the front lines of climate change, and while our politicians have dithered for a decade, we have dealt with the harsh realities of inaction," Farmers for Climate Action head Verity Morgan-Schmidt said.