President Trump informed Japan, South Korea and five other nations on Monday that they will face significantly higher tariff rates starting Aug. 1 unless they can broker new trade deals imminently with the United States.

The newly announced rates, communicated in letters to those nations’ leaders and posted on social media, marked a revival of Mr. Trump’s trade brinkmanship, with additional threats targeting other nations expected throughout the week.

The new tariff rates essentially replace the sky-high duties that the president announced in April. At the time, Mr. Trump quickly paused his so-called reciprocal levies for 90 days, mostly so his administration could broker favorable trade agreements around the globe.

But the White House has made minimal progress on what an official once described as a campaign to strike “90 deals in 90 days,” with the deadline set to lapse on Wednesday.

To buy more time, Mr. Trump is expected to sign an executive order on Monday that extends his initial pause, while sending notes to countries informing them of the new rates that they must start paying next month.

His initial battery of letters went to Japan, South Korea, Malaysia, South Africa, Kazakhstan, Laos and Myanmar. Both Japan and South Korea, which each represent about 4 percent of U.S. imports, face 25 percent tariffs on Aug. 1. Myanmar, which accounts for only a tiny fraction of goods imported into the United States, faces a newly announced tariff of 40 percent.

Mr. Trump also threatened to raise tariff rates even higher if any of the countries seek to retaliate with import taxes of their own or try to evade the U.S. duties by shipping through other nations.

In the coming days, the White House is expected to send additional letters to other countries, some of which will be subject to the tariffs outlined by the president in April.