Trump posted the two-page letters - addressed to the leaders of the Philippines, Brunei, Moldova, Algeria, Iraq, Libya and Sri Lanka - on his Truth Social platform on Wednesday.
None of the countries targeted in the letters is a major industrial rival to the United States.
The latest batch comes two days after he sent letters to 14 countries, including key allies Japan and South Korea, telling them to expect higher tariffs unless a new trade deal can be struck.
Algeria, Libya, Iraq and Sri Lanka face tariff rates of 30 per cent while Brunei and Moldova were threatened with 25 per cent and the Philippines 20 per cent.
Trump has been rolling out new tariff rules for goods entering the US since Monday, when he also extended a 90-day pause on his so-called reciprocal tariffs first announced on April 2.
The tariffs have sent heads spinning in corporate boardrooms and capitals.
Investors, however, seem to be taking the news in their stride as US stocks continue to push higher.
Trump said on Tuesday he will stick to his August 1 deadline, writing on Truth Social: "No extensions will be granted."
with AP
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