Canadian Prime Minister Justin Trudeau is facing one of the biggest tests of his political career as his deputy prime minister resigns.

Chrystia Freeland, who is also finance minister, left cabinet on Monday after clashing with Mr Trudeau on issues including how to handle possible Trump tariffs.

The shock move has given fresh scrutiny to Mr Trudeau's tenure, whose popularity has plummeted due to concerns about inflation and immigration.

He swiftly named longtime ally and public safety minister Dominic LeBlanc as Ms Freeland's replacement.

After being sworn in, Mr LeBlanc told reporters he and the prime minister were focused on the cost of living facing Canadians and on finding common ground with Trump on border security and economic issues.

"I'm very confident that we can continue to do the necessary work," Mr LeBlanc said.

New Democratic Party leader Jagmeet Singh, whose party Mr Trudeau's ruling Liberals have relied upon to stay in power, called on Mr Trudeau to resign earlier on Monday.

The main opposition Conservatives demanded an election.

Ms Freeland said Mr Trudeau had told her on Friday he no longer wanted her to serve as finance minister and offered her another role in the cabinet.

But she said in her resignation letter that the only "honest and viable path" was to leave the cabinet.

"For the past number of weeks, you and I have found ourselves at odds about the best path forward for Canada," Ms Freeland said.

Ms Freeland and Mr Trudeau had disagreed about a two-month sales tax holiday and $CAD250 ($275) cheques that were recently announced.

Ms Freeland said Canada was dealing with Trump's threat to impose sweeping 25 per cent tariffs and should eschew "costly political gimmicks" it could "ill afford."

"Our country is facing a grave challenge," she said in her letter.

A Liberal Party official said Ms Freeland was offered a position as minister in charge of Canada-US relations without a portfolio and without a department.

The official, who spoke on condition of anonymity, said the position would have been in name only and would not have come with any of the tools Ms Freeland previously had when she negotiated trade with the United States.

Ms Freeland, who chaired a Cabinet committee on US relations, had been set to deliver the fall economic statement and likely announce border security measures designed to help Canada avoid Trump's tariffs.

Trump has threatened to impose a 25 per cent tax on all products entering the US from Canada and Mexico unless the neighbours stem the numbers of migrants and drugs.

The statement shows a much larger deficit than expected for the fiscal year and more than $CAD1 billion for border security.

Mr Trudeau has said he plans on leading the Liberal Party into the next election, but some party members have said they do not want him to run for a fourth term, and Ms Freeland's departure is a huge blow.

No Canadian prime minister in more than a century has won four straight terms.

The federal election has to be held before October.

The Liberals must rely on the support of at least one other major party in Parliament because they do not hold an outright majority themselves.

If the New Democratic Party, or NDP, pulls support, an election can be held at any time.

Mr Singh said all options were on the table.

"He must acknowledge that and act accordingly.

"The departure of his most important ally, his finance minister, is the end of this government."

Mr Trudeau channelled the star power of his late father, former prime minister Pierre Trudeau, when he reasserted the country's liberal identity in 2015 after almost a decade of Conservative Party rule.

But Canadians are now frustrated by the rising cost of living and other issues, including immigration increases following the country's emergence from the COVID-19 pandemic.

AP