President Trump added on Wednesday to his growing list of countries that would face steep tariffs in the coming weeks if they fail to reach trade agreements with the United States, as he threatens to drag nations large and small into his trade war.

On his social media account, the president posted form letters informing seven countries, the Philippines, Sri Lanka, Moldova, Brunei, Libya, Iraq and Algeria, that they should prepare for double-digit tariff rates. Except for the name of the country and the tariff rate, the letters were identical to those he posted on Monday, which targeted 14 countries.

While those seven countries are considered minor trading partners, they join a list that includes powerhouses like Japan and South Korea. The move also suggests that the president is hewing to a global tariff strategy he announced in early April that punishes countries that sell more than they buy from the United States.

On Apr. 2, Mr. Trump announced he would impose a 10 percent tariff on all U.S. imports, plus higher tariffs on roughly 60 countries that sell more goods to the United States than they buy from it. He said that those trade imbalances were evidence that foreign countries had long mistreated the United States, an assertion economists have criticized.

The president had originally set July 8 as the last day for countries to sign trade deals with the United States to avoid those tariffs. At the urging of some of his advisers, on Monday he pushed the deadline back to Aug. 1.

Many countries are racing to try to sign trade deals, including major trading partners like the European Union and India. In April, Peter Navarro, the president’s top trade adviser, promised to sign 90 trade deals in 90 days. But it remains impractical for the United States to negotiate simultaneously with all of the countries the president has threatened with tariffs, something he acknowledged at the White House Tuesday.