Trump had immediately announced a 10 per cent across-the-board tariff on Friday after the court's decision, which found the president had exceeded his authority when he imposed an array of higher rates under an economic emergency law.
The new levies are grounded in a separate law, known as Section 122, that allows tariffs up to 15 per cent but requires congressional approval to extend them after 150 days.
No president has previously invoked Section 122, and its use could lead to further legal challenges.
Trade experts and congressional aides are sceptical that the Republican-majority Congress would extend the tariffs, given polls that show growing numbers of Americans blame the duties for higher prices.
In a social media post on Saturday, Trump said he would use that period to work on issuing other "legally permissible" tariffs.
The administration intends to rely on two other statutes that permit import taxes on specific products or countries based on investigations into national security or unfair trade practices.
"I, as President of the United States of America, will be, effective immediately, raising the 10% Worldwide Tariff on Countries, many of which have been 'ripping' the U.S. off for decades, without retribution (until I came along!), to the fully allowed, and legally tested, 15% level," he wrote in a Truth Social post.
Trump has shown little sign of backing off from his global trade war in the hours since the court's 6-3 decision.
Wendy Cutler, a former senior US trade official and senior vice president at the Asia Society think tank, said she was surprised Trump had not gone for the maximum Section 122 rate on Friday, but that his rapid-fire change underscored the uncertainty trading partners faced.
Trump, who often describes tariffs as his favourite word, has attacked individual justices in personal terms and insisted he retained the power to impose tariffs as he sees fit.
Trump has used the tariffs, or the threat of imposing them, to extract trade deals from foreign countries.
After the court's decision, Trump's trade representative, Jamieson Greer, told Fox News on Friday that those countries must honour agreements even if they call for higher rates than the Section 122 tariffs.
Exports to the US from countries such as Malaysia and Cambodia would continue to be taxed at their negotiated rates of 19 per cent, even though the universal rate is lower, Greer said.
The ruling could spell good news for countries like Brazil, which has not negotiated a deal with Washington to lower its 40 per cent tariff rate but could now see its tariff rate drop to 15 per cent, at least temporarily.
Trump's approval rating on his handling of the economy has steadily declined during his year in office, with 34 per cent of respondents saying they approve and 57 per cent saying they disapprove in a Reuters/Ipsos poll that closed on Monday.
