Trudeau's retort came as Donald Trump continued on Tuesday to taunt the United States' northern neighbour and close ally.
Trump has publicly mused for weeks about annexing Canada after he returns to the White House on January 20, and has called Trudeau the "governor" of the "Great State of Canada."
"There isn't a snowball's chance in hell that Canada would become part of the United States," Trudeau, who announced his resignation on Monday amid party infighting and growing unpopularity, wrote on X on Tuesday.
"Workers and communities in both our countries benefit from being each other's biggest trading and security partner."
There isn't a snowball's chance in hell that Canada would become part of the United States.— Justin Trudeau (@JustinTrudeau) Workers and communities in both our countries benefit from being each other's biggest trading and security partner.January 7, 2025
Hours earlier, President-elect Trump said he could use "economic force" to make Canada a state.
He made the threat at a rambling press conference at his Mar-a-Lago resort in Florida, in which he also declined to rule out using military force to gain control of the Panama Canal and Greenland.
Trump, however, said he would not go so far as to deploy the US military against Canada.
"Canada and the United States, that would really be something," he said.
"You get rid of the artificially drawn line and you take a look at what that looks like and it would also be much better for national security. Don't forget: We basically protect Canada."
Trump, a Republican, also said the US doesn't need Canadian vehicle exports because he would "rather make them in Detroit." He also said the US did not need Canadian lumber.
After winning the election against Democrat Kamala Harris in November, Trump quickly picked a fight with Ottawa by saying that he would impose a 25 per cent tariff on all products imported from Canada as soon as he took office.
He said the tariff would remain in place until Canada cracked down on the flow of drugs across the border.
Trudeau resigned on Monday as leader of his Liberal Party and as prime minister, although he will stay at the helm of Canada until his party selects his replacement.
Trump responded to the resignation by posting on his Truth Social site: "If Canada merged with the US, there would no Tariffs, taxes would go way down, and they would be TOTALLY SECURE from the threat of the Russian and Chinese Ships that are constantly surrounding them. Together, what a great Nation it would be!!!"
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