Liberal defector Corey Bernardi called the situation “intolerable”, comparing the Australian government to Italy’s politics, during proceedings.
However, he said he would not support the motion.
Earlier Greens Leader Richard Di Natale launched an attack on the government.
“It’s a disgrace. It’s utterly shameful. We haven’t had a stable government in this country for a decade now,” he said.
“I’ve got a 10-year-old boy, he’s seen half a dozen different prime ministers. We have politicians in this joint who are more concerned about themselves, about their own self-interest, than they are with governing the country.
“Just think, while the Liberal party has been tearing themselves apart. We’ve got 100 per cent of NSW that’s in drought right now, we’ve got the Great Barrier Reef on the brink of collapse, we’ve got floods in India.
"We’ve got a 12-year-old girl who is setting herself alight in Nauru. We’ve got kids who are in a catatonic state because they’ve given up hope, locked away in those offshore hell-holes. What’s the Liberal party doing? Focussing on vengeance. On payback.”
It comes after the government adjourned the House of Representatives, amid the growing leadership turmoil.
Opposition Leader Bill Shorten argued the coalition was now "irreparably split" and should hang their heads in shame.
Malcolm Turnbull has been told he no longer has majority support in the Liberal party room, with Peter Dutton expected to win a ballot once a meeting can be convened.
So far 13 ministers have resigned, stepping up pressure on the prime minister to quit.
Mr Shorten said adjourning the lower house was a clear admission of failure and the coalition should hang their heads in shame.
"The government may adjourn the parliament, but they cannot outrun the weight of failure of this government," he said.
"This is the ultimate admission of surrender, of a bankrupt government, of a failed government."
"If anyone needs to depart from this place, it is not the parliament, it is this government of Australia who has lost the confidence not just of its own backbench, not just of the opposition, you've lost the confidence of everyday
"Shame on you."
Manager of Opposition Business Tony Burke also ripped into the "extraordinary" development.
"What is happening right now is the government have decided this place has fallen apart so completely that they are dissolving the parliament for the day entirely," he told the lower house on Thursday.
Mr Burke said the coalition government was completely self-obsessed and had no regard for Australian voters.
"There will be no question time today because they don't know who their ministers are ... they don't know who their prime minister is," he thundered across the chamber.
"There will be no question time today because those opposite have stopped governing.
"If there was ever a government that had questions to answer, it's this mob."
The government has not sought to adjourn the Senate.