Trump said his order would be made under Section 122 of the Trade Act of 1974 and the duties would be over and above tariffs that are currently in place.
The statute allows the president to impose duties of up to 15 per cent for up to 150 days on any and all countries related to "large and serious" balance of payments issues.
It does not require investigations or impose other procedural limits.
The Supreme Court declared illegal his broad global tariffs imposed under the International Emergency Economic Powers Act, ruling that he had overstepped his authority under that law.
"We have alternatives, great alternatives" Trump said on Friday.
"Could be more money. We'll take in more money and we'll be a lot stronger for it."
Trump said his administration was also initiating several Section 301 unfair trade practices investigations "to protect our country from unfair trading practices of other countries and companies".
Trump's decision to lean on other statutes, including Section 122, while initiating new investigations under Section 301 had been widely anticipated.
But the 10 per cent tariffs he announced can only remain in effect for 150 days, and Section 301 investigations generally take months to complete.
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