The French president branded the prime minister a liar at the G20 summit, following Australia's decision to cancel a $90 billion submarine contract in favour of new nuclear-powered vessels as part of the AUKUS pact.
Meanwhile, Mr Turnbull also labelled Mr Morrison as dishonest, saying he had lied to him on multiple occasions while they were in government together.
However, when asked on Melbourne radio about whether he's lied while in public life, Mr Morrison rebuffed the claims.
"I don't believe I have, no," he told 3AW on Friday.
"That's politics, people take sledges at me all the time."
Mr Morrison said there wasn't a need for the Liberals to expel Mr Turnbull, as some in the party have sought.
"I don't see the need for that. I mean, if other's do that's fine, but it's just not something I think about," he said.
The prime minister also said he wasn't worried about the public criticism after backing out of the French submarine deal.
"I wasn't intimidated by the fact that that might upset some people and ruffle some feathers," he said.
"I was prepared to make the decisions that I had no doubt were going to draw some flak."
While confirming the election would be held next year, Mr Morrison said the government would start the campaign as underdogs.
"I think that's where we are now. I mean, that's not uncommon for incumbent governments," he said.