Prime Minister Justin Trudeau lands in Washington Monday morning where he will try to charm President Donald Trump – a man his polar opposite in nearly every way – to preserve Canada's close ties with its most important ally at one of the most unpredictable moments in the two countries' relationship.

The tête-à-tête at the White House is certain to be the most-watched meeting in decades between the leaders of two nations bound by free trade, defence and intelligence links as tight as any in the world.

Despite their sharply opposing politics and public images – Mr. Trudeau a sunny internationalist, Mr. Trump a bombastic protectionist – the Prime Minister has opted for a realpolitik approach to his far more powerful counterpart. He has avoided criticizing Mr. Trump directly and instead seems intent on convincing him that Canada can help advance his economic agenda.

Story continues below advertisement

Related: Trudeau visits Trump: A guide to their first meeting in Washington today

Analysis: In their first meeting, Trudeau needs to sell Trump on NAFTA

For subscribers: Why Trudeau's economic policies are disastrous in the era of Trump

What Mr. Trudeau will find when he meets Mr. Trump is far less certain.

The President campaigned on a promise to roll back free trade and has declared his intention to "speed up" a renegotiation of the North American free-trade agreement. Mr. Trump has spent the past 10 days in mounting frustration as the courts blocked his executive order freezing immigration from seven Muslim-majority countries. He has also, on occasion, tangled with allies during testy telephone conversations.

Two weeks ago, Mr. Trump surprised Australian Prime Minister Malcolm Turnbull, another leader of a long-time U.S. ally, by berating him about a refugee transfer agreement before abruptly ending the call. But he has also shown that he can be cordial and diplomatic with world leaders at key moments.

Mr. Trump is coming off a weekend of smiles and handshakes with Shinzo Abe – high-fiving and playing rounds of golf with the Japanese Prime Minister and giving him a key public assurance of U.S. support in the face of North Korea's latest missile test – demonstrating that, for all his bluster, the President is keen to publicly strengthen U.S. alliances.

Story continues below advertisement

"I just want everybody to understand, and fully know, that the United States of America is behind Japan, our great ally, 100 per cent," Mr. Trump told reporters on Sunday during a joint statement with Mr. Abe at the Mar-a-Lago club in Palm Beach, Fla. Japan was regularly the subject of Trump criticism for underpaying for the cost of keeping U.S. bases in the country, and involvement in the Trans-Pacific Partnership trade talks.

Mr. Trudeau is also certain to find a bifurcated reception among the U.S. political class.

The American centre left has constructed Mr. Trudeau as something of a saviour. A New York Times column last week gushed that Mr. Trudeau's Canada is "the finest example of the values of the Statue of Liberty" for letting in 40,000 Syrian refugees. And the Washington Post described Mr. Trudeau as "a leader of the liberal global resistance to President Trump" in an online piece last week.

The Breitbart news website favoured by Mr. Trump's supporters, meanwhile, portrays Mr. Trudeau as a scandal-plagued left-winger who hates the oil industry. One piece described him as the "handsome Bernie Sanders."

Both the left and right are certain to be disappointed with Mr. Trudeau's nice-guy approach to Mr. Trump. But observers argue it is the right choice, and the most likely strategy for maintaining the country's ties with its vastly more powerful neighbour.

"This is going to be one of the most-watched meetings, because it will set an example for other leaders of what to do," said Tamara Woroby, who teaches Canadian studies at Johns Hopkins University.

Story continues below advertisement

Canadian officials have been more pro-active than those of other countries in reaching out to their Trump administration counterparts since he took office, she said.

Prof. Woroby characterized Canada's approach as nice, but firm, and pointed to the balance struck by Foreign Affairs Minister Chrystia Freeland in her visit with her U.S. counterpart, Rex Tillerson, last week: For the most part, Ms. Freeland extolled the benefits to the U.S. economy of maintaining free trade and a warm relationship with Canada, but she also served notice that Ottawa would retaliate in the event of new border tariffs.

"It's very Canadian – pro-active but not aggressive. And nice, but nice doesn't mean soft or weak," Prof. Woroby said.

Analysts contend Mr. Trump's NAFTA anger is directed largely at Mexico, and Canada will escape the brunt of his ire.

David Wilkins, a former U.S. ambassador to Canada under ex-president George W. Bush, points out that Canada's trade relationship with the United States is very different from Mexico's. For one, trade between Canada and the United States is balanced, while the United States has a large trade deficit with its southern neighbour.

"NAFTA created large numbers of jobs through trade with Canada. It's put a lot of food on the table for American workers," Mr. Wilkins said. "Trudeau will be received very warmly. It will be a very productive meeting."

Story continues below advertisement

Mr. Wilkins said it helped that Mr. Trudeau played it cool during the U.S. election and didn't get involved.

Still, Mr. Trudeau will be dealing with a mercurial leader. In his court battle to get his immigration order reinstated, Mr. Trump has taken to attacking the courts themselves, accusing them of making the country unsafe. On Sunday, he dispatched a policy adviser, Stephen Miller, to hammer away at this point on the political talk-show circuit. "What the judges did … was to take power for themselves that belongs squarely in the hands of the President of the United States," he declared on NBC's Meet the Press.

Mr. Trump also took credit for a series of raids that scooped up hundreds of illegal immigrants last week, describing the people arrested as "criminals." "The crackdown on illegal criminals is merely the keeping of my campaign promise. Gang members, drug dealers & others are being removed!" he tweeted Sunday.

For all his planning and preparation, Mr. Trudeau cannot know exactly what he will face when he steps into the Oval Office.

"The only thing that's predictable about Donald Trump is his unpredictability," Prof. Woroby said. "Whether that's calculated – part of the art of the deal – or that's just his personality, no one going into a meeting with him knows the outcome."