The announcement came in the form of a letter published on Trumps social media platform Truth Social, along with additional threats of blanket tariffs of 15% or 20% on most trade partners.
Canadian Prime Minister Mark Carney said his government would continue to protect Canadian workers and businesses as they worked towards the new deadline.
Trump's letter is among more than 20 that the US president has posted this week to US trade partners, including Japan, South Korea and Sri Lanka.
Like Canada's letter, Trump has vowed to implement those tariffs on trade partners by 1 August.
A blanket 25% tariff has already been imposed on some Canadian goods, with the nation also hit hard by Trump's global steel, aluminium and auto tariffs - though there is a current exemption in place for goods that comply with a North American free trade agreement.
It is unclear if the latest tariffs threat would also apply to goods covered by the Canada-United States-Mexico Agreement (CUSMA).
Trump has also imposed a global 50% tariff on aluminium and steel imports, and a 25% tariff on all cars and trucks not build in the US.
He also recently announced a 50% tariff on copper imports, scheduled to take effect next month.
Canada sells about three-quarters of its goods to the US, and is an auto manufacturing hub and a major supplier of metals, making the US tariffs especially damaging to those sectors.
Trump's letter said the 35% tariffs are separate to those sector-specific levies.
"As you are aware, there will be no tariff if Canada, or companies within your country, decide to build or manufacture products within the United States," Trump stated.
He also tied the tariffs to what he called "Canada's failure" to stop the flow of fentanyl into the US, as well as Canada's existing levies on US dairy farmers and the trade deficit between the two countries.
"If Canada works with me to stop the flow of Fentanyl, we will, perhaps, consider an adjustment to this letter. These Tariffs may be modified, upward or downward, depending on our relationship with Your Country," Trump said.
President Trump has previously accused Canada - alongside Mexico - of allowing "vast numbers of people to come in and fentanyl to come in" to the US.
In his response on X, Carney said that Canada has made essential progress to "stop the scourge of fentanyl" in North America, and that his government was committed to continuing to work alongside the US to protect communities in both countries.
According to data from the US Customs and Border Patrol, only about 0.2% of all seizures of fentanyl entering the US are made at the Canadian border, almost all the rest is confiscated at the US border with Mexico.
Earlier this year, Canada also announced more funding towards border security and had appointed a fentanyl czar in response to Trump's complaints.
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