The fresh attacks President Trump aimed at Canada on Tuesday extended beyond imposing more tariffs on America’s neighbor and NATO ally, and laid out in the clearest terms yet his vision for annexing Canada and making it part of the United States.

Mr. Trump has made repeated comments about Canada becoming America’s 51st state since winning the election last November, and last month specifically told the country’s outgoing prime minister, Justin Trudeau, that he did not believe that the border treaty between the two nations was valid, The New York Times reported last week.

On Tuesday, as he announced his intention to double his planned tariffs on Canadian steel and aluminum, Mr. Trump publicly detailed much of his thinking.

“The only thing that makes sense is for Canada to become our cherished Fifty First State,” Mr. Trump wrote. “This would make all Tariffs, and everything else, totally disappear. Canadians taxes will be very substantially reduced, they will be more secure, militarily and otherwise, than ever before, there would no longer be a Northern Border problem.”

Echoing his private comments to Mr. Trudeau in that February call, he said about the border: “The artificial line of separation drawn many years ago will finally disappear.’’