Prime Minister Mark Carney of Canada said on Friday that he would travel next week to meet with President Trump for a high-stakes encounter between the two leaders of countries whose once-close friendship has collapsed amid a trade war and Mr. Trump’s threats to Canada’s sovereignty.

Mr. Carney also announced that King Charles III would visit Canada later this month, his first trip to the country since Charles’s coronation two years ago. The news of the trip, which was also announced by Buckingham Palace, is seen by analysts as a clear rebuke to calls by Mr. Trump to make Canada the 51st state because Charles is also Canada’s official head of state.

Mr. Carney, the former leader of the central banks of England and Canada, led the Liberal Party to victory in Monday’s national elections, in which dealing with Mr. Trump, his tariffs on Canadian exports and his repeated talk of making Canada another state were high on the minds of voters.

The Trump administration’s bellicose campaign against Canada, Mr. Carney said, has made it clear that Canada needs to negotiate new deals with the United States around a variety of issues, including economic and security alliances.

“Our old relationship, based on steadily increasing integration, is over,” Mr. Carney told reporters in Ottawa during his first news conference after the election. “The questions now are how our nations will cooperate in the future and where we, in Canada, will move on.”

Mr. Carney said he had asked Charles to deliver a speech on May 27 to open a new session of Canada’s Parliament because it “highlights Canada’s sovereignty as a nation.” When a new parliament convenes, the opening speech, which lays out the ruling party’s legislative agenda, is normally read by the governor general, the king’s representative in Canada.