The tit-for-tat came as federal parliament wrapped up for the year following a sitting fortnight dogged by nine coalition MPs crossing the floor, senior government members quitting and bills being abandoned.
"Hasn't the Morrison-Joyce government lost the ability to govern?" Labor leader Anthony Albanese asked the prime minister on Thursday.
Mr Morrison said the federal opposition was focused on "the slurs and sledges and trivialities of politics".
"Their big problem with me, as prime minister ... is apparently I go home for Father's Day, I have a holiday with my family, and I go to church on a Sunday. Get over it, a lot of Australians do," he said.
Labor MPs later rejected any suggestion they had ridiculed Mr Morrison's churchgoing, but noted the prime minister had "abandoned" people in bushfire areas when he holidayed in Hawaii in 2019.
The question time stoush came after a messy political day in which Education Minister Alan Tudge stood aside pending an inquiry called by Mr Morrison, and colleagues of Christian Porter rallied around the retiring former minister.
Mr Tudge rejected claims he mistreated a former staffer with whom he had a consensual affair in 2017 and vowed to co-operate with the inquiry.
Mr Porter has had a a scandal-plagued year in which he was accused of a historical rape he strenuously denies.
"He's been hounded out of politics in a very unfair and unjust way. But that's the nature of public life in the year 2021, unfortunately," Defence Minister Peter Dutton said.
Health Minister Greg Hunt, meanwhile, received a standing ovation from both sides of the chamber when he announced his retirement on Thursday after 20 years representing the Victorian seat of Flinders.
"Thank you for honouring our party, thank you for honouring your family, and thank you for honouring yourself in the way you have conducted yourself," Mr Morrison said of the minister.
Labor whip Chris Hayes also received applause as he ended a 16-year parliamentary career.
Summing up the year, Mr Albanese said Labor - which has consistently led the coalition in recent polls - was "competitive" ahead of an election due by May.
"It's a tough time to be in opposition during a pandemic," he said.
"Most (state and territory) oppositions around the country ... have not been competitive in the lead-up to an election.
"We will continue to hold the government to account and put forward a constructive alternative offer to the people of Australia."
Mr Morrison, who told a partyroom meeting the coalition was the "underdog" in the election, urged his colleagues to "rest up" over the Christmas break.
"We will come together to ensure Australia continues to have a strong government that Australians deserve and need," he said.
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