President Trump signaled on Sunday that he would pursue new tariffs on the powerful computer chips inside smartphones and other technologies, just two days after his administration excluded a variety of electronics from the steep import taxes recently applied on goods arriving from China.

The push came as Mr. Trump’s top economic advisers scrambled to explain their shifting strategy, after having insisted for weeks that they would shield no company or industry from any of the fees they have levied in a bid to reset U.S. trade relationships.

The reprieve for technology companies arrived in the form of a Customs and Border Protection rule issued late Friday that spared high-tech imports from Mr. Trump’s so-called reciprocal tariffs, including those on China. While the president paused a set of punishing levies on nearly 60 countries last week, his administration has forged ahead with a new 145 percent tax on Chinese exports, announcing it after Beijing retaliated against the United States.

The exclusions in the C.B.P. rule covered a wide slate of products, such as computers, smartphones, modems and flash drives, and it represented a major victory for Apple, and other U.S. technology giants, which rely on Chinese factories to help manufacture important components and popular devices. Apple executives had even been in contact with Trump administration officials about the Chinese tariffs in recent days, according to two people with knowledge of the company’s efforts. The company declined to comment.

But on Sunday, Mr. Trump and his top aides cast the exemptions in a different light, framing them as only a temporary break while the government prepares more targeted import taxes on key technologies. The administration is expected to take the first step toward enacting the new tariffs as soon as next week, opening an investigation to determine the effects of semiconductor imports on national security.

The approach appears to mirror the process that yielded Mr. Trump’s tariffs on other specific products and sectors, including the high fees he imposed on foreign cars and auto parts this year. On social media, the president signaled Sunday that the scope of his next inquiry would be broad, “taking a look at Semiconductors and the WHOLE ELECTRONICS SUPPLY CHAIN in the upcoming National Security Tariff Investigations.”

“NOBODY is getting ‘off the hook’ for the unfair Trade Balances, and Non Monetary Tariff Barriers, that other Countries have used against us, especially not China which, by far, treats us the worst!” Mr. Trump added.

Howard Lutnick, the commerce secretary, said earlier Sunday on ABC’s “This Week” that Mr. Trump could announce new tariffs “in the next month or two” that would target not only semiconductors but also pharmaceutical imports, another priority for the administration.

Kevin Hassett, the director of the White House National Economic Council, told CNN’s “State of the Union” that it was “always the case” that some of these high-tech imports would be subject to their own tariffs, separate from those broadly imposed on countries in response to their trade practices.

“Semiconductors are a key important part of a lot of defense equipment,” Mr. Hassett added, saying, “I don’t think anything really should be a surprise.”

And Jamieson Greer, the U.S. trade representative, described the move on CBS’s “Face the Nation” as more of a mechanical change, saying of semiconductors that it is “not that they won’t be subject to tariffs” but that they are being done under a “different regime.”

The Trump administration had already excluded various types of semiconductors from the reciprocal tariffs as of April 2. But the chaotic changes in tariffs and exclusions in recent days bewildered businesses that depend on trade with China. Some investors and chief executives publicly praised the decision to walk back tariffs on electronics, which represent roughly a quarter of U.S. imports from China.

“A willingness to adjust a strategy based on new facts and data is a sign of the strength of a leader,” Bill Ackman, the chief executive of the hedge fund Pershing Square, wrote on social media. “It is not an indication of weakness.”

Still, there appears to be no quick end to the trade conflict with China in sight. And the potential for new tariffs on chips threatened to cast another pall over the tech industry, even as major lobbying groups representing Intel, Nvidia and other companies have encouraged the Trump administration to strike trade deals that ultimately lower trade barriers globally.

Asked about the possibility of upcoming tariffs on chips on Saturday, Mr. Trump said, “I’ll give you that answer on Monday.”

“We’ll be very specific,” he added. “But we’re taking in a lot of money. As a country we’re taking in a lot of money.”

Dan Ives, an analyst for Wedbush Securities, said in a note to investors on Sunday that “the mass confusion created by this constant news flow out of the White House is dizzying for the industry and investors and creating massive uncertainty and chaos for companies trying to plan their supply chain, inventory and demand.”

Ultimately, new taxes on chip imports could make it more expensive for U.S. companies to produce smartphones and other devices, cutting into their profits or forcing them to raise prices on American consumers. For Apple, in particular, the tit for tat between the United States and China caused the tech giant to lose more than $770 billion in market capitalization in just the opening days of Mr. Trump’s trade war.

Since then, the two nations have continued to retaliate against each other, causing financial markets around the world to whipsaw in the face of a persistent and costly standoff. U.S. consumers even appeared to rush out to purchase new iPhones last week, anticipating that a protracted trade conflict could push up prices.