After Mr. Trump announced the moves, China’s Ministry of Commerce said that it was proposing tariffs of its own on 128 products from the United States, like nuts, wine and pork, that it valued at about $3 billion. China urged the Trump administration to resolve differences through dialogue to “avoid damage to the broader picture of Chinese-U.S. cooperation.”

The president’s actions fulfill his frequent campaign pledge to demand fairer trade deals with nations around the globe and to retaliate against trading partners if the United States does not secure better agreements.

“We have one particular problem,” the president said before signing an order that will impose tariffs on hundreds of Chinese products, from shoes and clothing to consumer electronics. “We have a tremendous intellectual property theft situation going on.”

The sanctions reflect a shift in relations between the two economic giants, which for years engaged in highly structured dialogues to try to reach agreement on economic and security issues. But the White House now views those dialogues — and the agreements they produced — as largely hollow promises by the Chinese.

Rather than trying to draw China into the rules-based international economic order — a policy that dates back to Richard M. Nixon and Henry A. Kissinger — the United States now regards China as a strategic competitor, bent on eroding American security and prosperity.