Kudlow said the Trump administration remains interested in the WTO and is working to resolve some of its trade disputes through the organization, but maintained its rulings would not determine US policies.
CNN said Wednesday that Trump invoked the War of 1812 in a testy phone call with Trudeau on May 25 about the burgeoning trade row.
In April, Canada tried to address what Trump said were concerns about Chinese steel and aluminum being dumped into Canada and then being shipped into the United States.
Trump and the White House have not commented publicly on the report.
"There may be disagreements", Kudlow added.
"There may be disagreements, I regard this as much like a family quarrel".
Canadian Foreign Affairs Minister, Chrystia Freeland has already indicated the feds feel insulted by the tariff, sentiments that have been echoed by other trade and business partners. Trump is unlikely to back away from the nationalistic policies that have frustrated and unnerved allies but which he sees as key promises to his most loyal voters.
The EU told the World Trade Organization last month it planned to enact tariffs on more than 3 billion US dollars worth of USA goods, including agricultural products such as rice, corn, dry kidney beans, cranberries, tobacco and orange juice.
Some U.S. industry analysts said it would not be easy, or cheap, for Mexico to switch to suppliers further afield than its northern neighbour.
The country reacted quickly after Washington said it was moving ahead with tariffs on aluminum and steel imports from Canada, Mexico and the European Union.
When asked whether or not they think Trump's actions will cause a trade war, 62 percent of participants said it is likely, with 20 percent saying that result is unlikely and 19 percent stating they had no opinion.
But the organization said this new tariff now puts that goal in doubt.
After 40 years of striving to solidify global cooperation, the G-7 now faces a tough test.
"This upcoming summit won't be an easy one, and the leadership of the Canadian government is very much counted upon", Kimihiro Ishikane, Japan's ambassador to Canada, said in an interview.
While trade is expected to dominate, Trudeau also wants to focus on gender equality and climate change.
The meeting of Group of Seven finance ministers and central bank governors, held in Canada last weekend, revealed a sharp rift between the United States and the other six nations over trade issues. "Those days are over", the statement said.
To see why these three USA allies are so upset, one need only look at the biggest suppliers of US metals. After years of decline by U.S. smelters Canada has become America's go to supplier of the affordable, in-demand metal.
Trudeau and US President Donald Trump. "We take him at his word". They are our ally.
According to CNN's sources familiar with the conversation, Trudeau pressed Trump on his national security justification for the tariffs, to which Trump replied: "Didn't you guys burn down the White House?"
"For better or worse, Mexico has become as much dependent on the USA for the pork that it feeds its people as the US has become dependent on Mexico", said Altin Kalo and agricultural economist with Steiner Consulting Group in Manchester, New Hampshire.
"This is deeply offensive to Canadians", Alden said.
Trump does not intend to withdraw from NAFTA, National Economic Council Director Larry Kudlow said on "Fox & Friends".