President Trump on Tuesday threatened to rename Lake Ontario as Lake America, the latest in a stream of provocations he has hurled at Canada and its leaders as a trade war heats up.

“The United States is giving serious consideration to changing the name of Lake Ontario to Lake America,” Mr. Trump wrote in a social media post, rationalizing the change because “we don’t expect to be doing much business with Ontario any longer.”

The president’s post was his latest verbal attack on Canada as the two countries exchange increasingly punitive threats over taxes on trade. The trade dispute escalated over the weekend as talks between the two neighboring countries broke down.

Last week, Mr. Trump announced that U.S. negotiators had reached a deal with the Canada to head off his plans to impose 50 percent tariffs on a range of Canadian goods.

But Canada, the United States’ second-largest trading partner and longtime ally, said the offer on the table was a “bad deal” and tariffs on some $20 billion in goods came into effect Saturday. On Tuesday, Prime Minister Mark Carney of Canada announced retaliatory tariffs of up to 50 percent on hundreds of American products “dollar for dollar,” after Mr. Trump threatened more duties on steel, cars, trucks and related parts beginning next year.

Mr. Trump also has taken aim at the premier of Ontario, Doug Ford, who had been one of the driving forces behind Ottawa’s opposition to the deal the United States had proposed. Mr. Ford told Mr. Carney that the terms were unfavorable to Canadian car and steel manufacturers and that his province wouldn’t comply with a requirement to restore sales of U.S.-made alcohol, according to people familiar with the negotiations.

In an earlier social media post on Monday, Mr. Trump quipped that Mr. Ford was “overall unimpressive” and warned that “someone should get these clowns to “fall in line” or, the consequences for Canada will be far WORSE!”

To drive his point home, Mr. Trump also posted a marked-up map of the lake, the smallest of the five Great Lakes and which separates the Canadian province of the same name and New York State. A big, red X crossed out the words “Lake Ontario” and, in an oversize gold font, “Lake America” replaced them, flanked by an American flag.

The name change is reminiscent of Mr. Trump’s move to rename the Gulf of Mexico as the Gulf of America, a change he demanded by executive order on the first day of his second term.

Historical references to Lake Ontario predate the founding of either the United States or Canada. The name is thought to be derived from an Indigenous term meaning either “beautiful water” or “great lake.”