It was the latest of more than 20 such letters issued by Trump since Monday, as he continues to pursue his trade war threats against dozens of economies.
The letter on Thursday came despite what had been warming relations between Trump and Carney.
The Canadian leader visited the White House on May 6 and held a cordial meeting with Trump in the Oval Office.
They met again at the G7 summit last month in Canada, where leaders pushed Trump to back away from his punishing trade war.
In an interview with NBC News published on Thursday, Trump also said that other trading partners that had not yet received such letters would likely face blanket tariffs.
“Not everybody has to get a letter. You know that. We’re just setting our tariffs,” Trump said in the interview.
“We’re just going to say all of the remaining countries are going to pay, whether it’s 20 percent or 15 percent. We’ll work that out now,” Trump was quoted as saying by the network.
In recent days, he also set new tariffs on a number of countries, including allies Japan and South Korea, along with a 50 percent tariff on copper.
On Friday, Myanmar, which was also hit by stiff Trump tariffs, pleaded with Trump for a reduction in the 40 percent tariff rate, with ruling Senior General Min Aung Hlaing saying he is ready to send a negotiation team to Washington if needed, according to state media.
Meanwhile, the Philippines’ Secretary of Foreign Affairs Theresa Lazaro told Reuters news agency in Malaysia that Philippine President Ferdinand Marcos Jr will meet Trump in Washington DC later this month to discuss the 20 percent tariffs imposed on Manila, as well as mutual defence issues.
