"Be Strong, Courageous, and Patient, and GREATNESS will be the result!," he wrote on Truth Social, his social media platform.
Trump accused other countries of "taking advantage of the Good OL' USA!" on international trade and said "our past 'leaders' are to blame for allowing this".
The Republican president has insisted his tariffs are necessary to rebalance global trade and rebuild domestic manufacturing.
He has singled out China as "the biggest abuser of them all" and criticised officials in Beijing for increasing their own tariffs in retaliation.
The European Union was offering the United States an agreement on the reciprocal lifting of all tariffs on industrial goods, European Commission President Ursula von der Leyen said on Monday.
The EU remains ready to negotiate a solution despite the US tariff decisions, von der Leyen said, after an exchange with representatives from the steel and metals industries.
The US imposed tariffs of up to 25 per cent on imports of steel, aluminium and related derivative products from the EU and other trading partners in March.
On Saturday, the US government additionally introduced universal tariffs of a minimum of 10 per cent on imports from almost all its trading partners.
Significantly higher levies will apply for some countries, depending on trade deficits, with goods from the EU facing a 20 per cent tariff from Wednesday.
United Kingdom Prime Minister Keir Starmer said on Monday the government would back its car manufacturers "to the hilt" after Trump on April 3 imposed a 25 per cent tariff on car imports.
Starmer described the tariffs as a "huge challenge".
Trump said on Sunday he wouldn not back down from his tariffs despite the turmoil in the global markets.
"Sometimes you have to take medicine to fix something," Trump said.
Goldman Sachs issued a new forecast saying a recession has become more likely even if Trump relents from his tariffs.
The financial firm said economic growth would slow dramatically "following a sharp tightening in financial conditions, foreign consumer boycotts and a continued spike in policy uncertainty that is likely to depress capital spending by more than we had previously assumed".
On Monday, the president is scheduled to welcome the Los Angeles Dodgers to the White House to celebrate their World Series victory.
He is also meeting with Israeli Prime Minister Benjamin Netanyahu and they are expected to hold a joint press conference in the afternoon.
with DPA and Reuters
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