Trump's comments made on Monday sent US stocks down sharply in late afternoon trading. The Mexican peso and Canadian dollar both fell following his remarks.
"They're going to have to have a tariff. So what they have to do is build their car plants, frankly, and other things in the United States, in which case they have no tariffs," Trump said at the White House.
He said there was "no room left" for a deal that would avert the tariffs by curbing fentanyl flows into the United States.
Trump also reaffirmed that he will increase tariffs on all Chinese imports to 20 per cent from the previous 10 per cent levy to punish Beijing for failing to halt shipments of fentanyl to the US.
The president said in an order that China "has not taken adequate steps to alleviate the illicit drug crisis."
CEOs and economists say Trump's tariffs on Canada and Mexico, covering more than $US900 billion ($A1.4 trillion) worth of annual US imports, will deal a serious setback to the highly integrated North American economy.
The tariffs are scheduled to take effect at one minute past midnight on Tuesday US time, the Trump administration confirmed in Federal Register notices.
At that point, the US Customs and Border Protection agency will begin collecting 25 per cent Canadian and Mexican goods, with a 10 per cent duty for Canadian energy.
Mexico's economy ministry said that there would be no public response until President Claudia Sheinbaum's regular morning press conference on Tuesday. She has vowed to respond, saying: "We have a plan B, C, D."
Canadian Foreign Minister Melanie Joly told reporters that Ottawa was ready to respond, but offered no specifics.
Ontario Premier Doug Ford told NBC that the US tariffs and Canada's retaliation would be "an absolute disaster" for both countries.
"I don't want to respond but we will respond like they've never seen before," Ford said, adding that Michigan auto plants would likely shut down within a week and that he would halt nickel shipments and cross-border transmission of electricity from Ontario to the US.
"I'm going after absolutely everything," Ford said.
China's commerce ministry on Tuesday vowed countermeasures against Washington's decision and urged the US to "immediately withdraw" its tariffs, which it described as "unreasonable and groundless, harmful to others."
The state-backed Global Times newspaper earlier said Beijing's countermeasures would most likely target US agricultural and food products.
The Dow Jones Industrial Average fell 649.67 points, or 1.48 per cent, the S&P 500 lost 104.78 points, or 1.76 per cent, and the Nasdaq Composite dropped 497.09 points, or 2.64 per cent.
Automaker shares fell sharply, with General Motors, which has significant truck production in Mexico, down 4 per cent and Ford falling 1.7 per cent.
Mexico, after avoiding the first round of Trump's tariffs by striking a last-minute deal to send thousands of troops to its northern border, has stepped up anti-drug efforts and hinted at new measures on imported Chinese goods.
According to the Centers for Disease Control and Prevention, 72,776 people died from synthetic opioids in 2023 in the US, chiefly from fentanyl.
Representative Suzan DelBene, a Democrat from the state of Washington, said the decision to proceed with tariffs on Canada and Mexico would cost American families thousands of dollars at the grocery store, gas station and pharmacy counter.
"No president should be able to raise taxes without a vote in Congress," she said in a statement.
White House trade adviser Peter Navarro, however, said on Monday that the inflationary impact from any tariffs would be "second-order small" and that he did not expect the president to waver on the measures.
