The turning outward of American governors was on prominent display at the National Governors Association retreat in Providence, R.I., last week. There, Prime Minister Justin Trudeau of Canada spoke on Friday, the first foreign leader to address the group. Gov. Terry McAuliffe of Virginia, a Democrat who is chairman of the governors association, said representatives were present from a number of other countries, including China, Japan, Mexico and Vietnam.

In addition, aides to a number of governors, including Mr. Brown and Mr. Inslee, conferred privately to plan for a climate conference in Bonn, Germany. Mr. Trudeau framed his remarks to the group as a tribute to the relationship between the United States and Canada, highlighting shared goals on climate and national security, and urging governors not to support a “race to the bottom” in the form of trade protectionism. Using the same favorable adjectives most American governors apply to themselves, Mr. Trudeau hailed them for pursuing economic prosperity with a “pragmatic approach that crosses party lines.”

“Whether Republican or Democrat, in this economy, that’s likely your very first priority,” he said. “Guess what: It’s my first priority as well.”

The Canadian leader’s friendship mission followed months of stepped-up contact between American governors and Canadian political and business leaders after Mr. Trump’s election.

Gov. Phil Scott of Vermont, who has made multiple trips across the Canadian border since his election in November, said he had made it a priority to put the state’s longstanding economic partner at ease.

Mr. Scott, who is one of two Republican governors to join the climate initiative, along with Charlie Baker of Massachusetts, said that in Canada there had been a mood of “concern, especially initially, about this new administration.”

“They needed some reassurance that we were there fighting on their behalf, and on our behalf as well,” Mr. Scott said. “We wanted to make sure that we communicated that and gave them, the Canadians, reassurance that we’re there for them.”