US President Donald Trump has threatened to impose higher tariffs on countries that "play games" with recent trade deals, after the Supreme Court last week blocked many of the sweeping global levies.

His warning came as countries around the world said they were evaluating what tariffs and trade deals would stand following the decision, which struck down the bulk of tariffs Trump imposed last year.

The European Union said on Monday it would suspend its ratification of a deal struck over the summer.

India also said it would defer previously scheduled talks to finalise a recent agreement.

Writing on social media, Trump warned countries against using the ruling to back away from trade commitments made in response to last year's tariffs.

"Any Country that wants to 'play games' with the ridiculous Supreme Court decision, especially those that have 'Ripped Off' the U.S.A. for years, and even decades, will be met with a much higher Tariff, and worse, than that which they just recently agreed to," he wrote on Truth Social. "Buyer beware."

The back-and-forth is an indication of the chaos sparked by the Supreme Court's Friday ruling striking down tariffs unveiled by Trump last spring under the 1977 International Emergency Economic Powers Act (IEEPA).

The court said that law did not authorise the president to impose the tariffs, which are a tax on imports paid by businesses bringing goods into the country.

Trump responded by announcing a new 10% global tariff using a different law, which he quickly raised to 15%. That measure, which exempts some products, was set to come into force on Tuesday.

But many countries said they remained uncertain about the status of deals negotiated in the wake of Trump's initial tariff measures, when many sought lower levies on their goods in exchange for promises of investment or other concessions meant to make it easier for American firms to do business abroad.

The UK on Monday said it was pressing US officials for answers about whether its deal, which had set tariffs at 10%, below the 15% rate Trump announced on Saturday, would hold.

"I recognise the uncertainty the latest announcement from the US has created," UK Business and Trade Secretary Peter Kyle said in a statement, adding that "all options" were on the table as the UK seeks to protect businesses and the public.

Bernd Lange, chair of the European Parliament's International Trade Committee, said the committee had suspended its approval of the deal the US and EU had approved in July while it sought clarity.

"The situation is now more uncertain than ever," he said.

The White House has insisted that its approach to trade will not change as a result of the ruling, as it turns to other laws to impose the duties.

Trump on Friday deployed Section 122, a never-used law that allows the president to impose tariffs for 150 days without congressional approval.

He also ordered officials to start investigations under Section 301, a separate trade law that allows the president to impose tariffs in response to specific "unfair" trade practices.

The new tariffs are expected to stand alongside separate, previously announced tariffs Trump has imposed on specific items, such as steel, aluminium and cars, which were unaffected by the court's ruling.

"We found ways to really reconstruct what we're doing," US Trade Representative Jamieson Greer told on ABC News on Sunday.

"The legal tool to implement it - that might change, but the policy hasn't changed."

In a separate interview with CBS News on Sunday, Greer said that the White House would "stand by" the trade deals it had struck. "We expect our partners to stand by them," Greer added.

Shares in the US fell on Monday, with the S&P 500 down about 1%, weighed down in part by trade uncertainty, which many analysts and businesses expect to persist.

The new 15% tariffs are due to expire after 150 days, unless Congress votes to extend them.

Senate Democratic minority leader Chuck Schumer warned on Monday that Democrats would block any attempt to extend the duties. Trump's tariffs are also unpopular with some Republicans.

Schumer said in a statement: "Democrats will not go along with furthering Trump's economic carnage."

On Monday, Trump wrote on social media that he did not need Congress's approval for tariffs.