Mr Trump, who has vowed to protect United States industry and workers from what he describes as unfair global competition as part of an "America First" agenda, is due to hold bilateral meetings with Mr Trudeau and French President Emmanuel Macron during the summit, Mr Kudlow said.
The other G7 members - Canada, France, Germany, Italy, Japan, and the United Kingdom - are likely to bash Trump's recent tariffs and trade restrictions.
Despite his "bromance" with Trump, he too let the US leader know he's not pleased with the new tariffs on steel and aluminum.
Trump fired back soon after on Twitter, addressing both leaders directly, saying they were charging "massive tariffs" on United States goods and had erected other trade barriers.
"I think this is a really important moment for us to come together and work on big issues", he said.
A French presidency official said that while G7 members would raise their unhappiness over the tariffs with Trump, they would not deliver an ultimatum that he drop them because the summit "isn't the place where you negotiate things like that". One of the largest reasons for Trump's reluctance is the host country, the report said.
Sources claimed that the president invoked the War of 1812 when his Canadian counterpart asked him how he could justify the tariff change as a "national security" issue, which the administration had done under a 1962 trade law.More news: French Open 2018: Muguruza dumps Sharapova to reach semis
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"The world economic order is under pressure, under attack", Canadian Trade Minister Francois Philippe Champagne said.
In private, the trade battle has strained a once-cheery relationship between the two leaders. "France and North Atlantic Treaty Organisation - this is ridiculous to think that they could be a threat to the United States' security", Trudeau said. "We can't engage in a trade war against friends", Mr. Macron said.
The White House subsequently announced the president would be leaving on Saturday, before the summit formally ends, to fly to Singapore for a meeting with North Korean leader Kim Jong Un.
France has joined Germany in warning President Donald Trump that it won't sign a joint statement of the Group of 7 at the summit in Quebec this week without major concessions from the USA, a French official in the president's office said.
"If I can get the president to actually realize that what he's doing is counterproductive for his own goals as well, perhaps we can move forward in a smarter way".
Last week, Trump chose to end those exemptions, and the tariffs went into effect on June 1.
The United States is reportedly preparing to unleash another round of tariffs on Canada as retribution for its Can$16.6 billion (US$12.9 billion) in tariffs on USA goods.
Treasury Secretary Steven Mnuchin tried to brush off the statement following the summit.