Justin Trudeau was all smiles, handshakes and encouraging words at the White House during his first meeting with Donald Trump, despite a slightly frosty start for the US-Canada relationship.

The leaders posed for a photo in the Oval Office in reported near silence as the cameras clicked.

“I think they want a handshake,” Mr Trump said.

Later in the Cabinet Room, Mr Trudeau pulled out a chair for the President’s eldest daughter, Ivanka Trump, and thanked her for organising the roundtable of women executives to discuss how to “create paths” for entrepreneurial success.

The Canadian leader’s visit to Washington, including a lunch and meetings with House Speaker Paul Ryan and Senate majority leader Mitch McConnell, will be viewed as critical for strengthening relations and maintaining daily, cross-border trade of around $2bn.

Behind the smiles and formalities, the liberal Canadian leader and the conservative American populist were set to discuss two polarising issues: refugees and workplace gender equality.

Mr Trudeau warned Canada would "not agree on everything", referring to Mr Trump’s executive order to ban people from seven Muslim-majority countries.

The ban, which was signed on 27 January, confused Canadians and those with dual nationalities, as well as visa and green card holders.

Mr Trudeau posted a photo on the day of the ban, kneeling beside a child refugee – one of 40,000 Syrian refugees last year – with the caption “Welcome to Canada”. The US has taken in 12,500.

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While Mr Trudeau said that he would continue to welcome refugees without compromising national security, Mr Trump insisted that he wanted to “keep out the very bad dudes”.

Mr Trudeau added that while the two nations had “fought and died together”, there “have been times where we have differed in our approaches and that's always been done firmly and respectfully”.

He added: “The last thing Canadians expect is for me to come down and lecture another country on how they choose to govern themselves. My role and responsibility is to continue to govern in such a way that reflects Canadians' approach and be a positive example in the world.”

The leaders’ also announced a joint initiative, the Canada-United States Council for Advancement of Women Entrepreneurs and Business Leader, but their stances on womens’ rights could also be seen as polar opposites.

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While Mr Trudeau created a gender-balanced cabinet in 2015 and has often declared himself a feminist, Mr Trump has not been so warmly regarded by proponents of gender equality.

Alongside multiple accusations of sexual assault, which Mr Trump has strongly denied, the President also admitted that he regretted hiring his first wife, Ivana Trump, and bragged that he had never changed a diaper.

“We need to make it easier for women to manage the demands of having a job and a family,” Mr Trump told the roundtable.

One of his first acts as President was to reinstate the Mexico City Policy, which bans US aid for any foreign organisation that even talks about abortion. He is pro-life and critics fear he will roll back women's reproductive rights, preventing them from being able to contribute fully to the workforce if they cannot make decisions about their own bodies.

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The White House gathering was expected to discuss maternity leave. Under a proposal crafted by his daughter, Mr Trump promised to provide six weeks of paid maternity leave if a woman’s company did not offer any form of cover, and the government would pay for the multi-billion dollar bill by targeting workplace insurance fraud.

“We need to think about how we level the playing field for this generation and the next,” said Ivanka Trump at the meeting.

In Washington on Monday, Mr Trudeau was accompanied by several key Canadian ministers, but not his wife, Sophie Gregoire Trudeau. Around 6pm, he was scheduled to fly back to Ottawa.

Mr Trump had insisted that their conversation was “very, very productive”.

Mr Trudeau can only hope he struck the right note with his neigbour after a fair share of controversy in recent months – Mr Trump was widely criticised for not making a public statement about the Quebec Mosque shooting, which was carried out by a white man against Muslims, killing six. Mr Trump did call Mr Trudeau on 30 January to offer his condolences.