US President-elect Donald Trump took a light jab at his Canadian counterpart on Tuesday, referring to Justin Trudeau as the "governor" of the "Great State of Canada".

In an early morning social media post on Tuesday, he references a dinner the pair had in late November at Trump's Florida estate, Mar-a-Lago.

Prime Minister Trudeau travelled to meet Trump following a threat by the president-elect to impose a blanket 25% tariff on Canadian goods when he takes office in January.

Trump says in the post he hopes the pair can "continue our in-depth talks on Tariffs and Trade, the results of which will be truly spectacular for all".

Canada, a country of 40 million people, is one of America's largest trading partners and it sends about 75% of its total exports to the US. The two countries also share deeply integrated supply chains.

On Monday, Trudeau told the Halifax Chamber of Commerce that Canada will respond to the tariffs if the Trump administration moves ahead with the threat following Trump's 20 January inauguration.

Trudeau noted Canada is still considering the "right" way to respond, but referenced retaliatory tariffs Ottawa imposed when the first Trump administration slapped levies on steel and aluminium.

"Our responses to the unfair steel and aluminium tariffs were what ended up lifting those tariffs last time," he said.

Ottawa placed tariffs on both metals, as well as over 250 US goods including beer kegs, whiskey and orange juice - designed to politically pressure the US and make it take notice of the affect on cross-border trade.

Trudeau on Monday called those counter-measures "carefully targeted" and "politically impactful to the president's party and colleagues".

It allowed Canada - which is economically much smaller than the US - to "punch back in a way that was actually felt by Americans", he said.

The president-elect's threatened the blanket tariff against Mexico as well unless the two nations secured their shared borders with the US.

The number of crossings at the US-Canada border is significantly lower than that at the southern border, according to US Border Patrol data on migrant encounters, as is the amount of fentanyl seized.

Trudeau said while he takes the potentially economically devastating tariff threat seriously, Canadians should not "freak out".

The president-elect's approach is often to "destabilise a negotiating partner", he said.

Trudeau is set to meet the leaders of Canada's provinces and territories for a second time on Wednesday to discuss the plan to approach negotiations with the US.

Tuesday's "governor" quip is not the first time Trump has needled Canada.

At Mar-a-Lago, Trump remarked that Canada should become the 51st US state - something that was "in no way a serious comment", said Public Safety Minister Dominic Leblanc, who accompanied Trudeau to the dinner.

"The president was telling jokes, the president was teasing us," he told reporters early this month.