Mr. Pompeo’s 60-day deadline could be seen as a gesture toward European worries, especially from Germany, which ever since the Cold War has been anxious about becoming the battlefield for strategic competition between the United States and Russia. In a news conference on Tuesday, Mr. Pompeo said that “our European partners” had asked for “an extended period,” and added, “We believe this is the right outcome.’’

While the Trump administration pointed to years of treaty violations by Russia, there is another reason it wants to abandon the deal: The pact constrains the United States from deploying new weapons to respond to China’s growing militarization of the South China Sea.

Because China is not a signatory to the treaty, it has faced no limits on developing intermediate-range nuclear missiles, which can travel thousands of miles. Most of China’s missiles fall within the range of weapons prohibited by the treaty. The treaty does not ban intermediate missiles launched from the sea or from airplanes.

The agreement was negotiated after a long, wrenching debate among NATO allies in the 1980s about how to counter the Russian deployment of SS-20 missiles, designed to hit Europe. In the end, the Europeans agreed to deploy American Pershing II missiles on their soil.

That led to the bilateral American-Soviet treaty, which banned all such weapons.

NATO’s anxiety now stems from the ability of new Russian mobile missile launchers to fire both missiles that remain within the limits of the treaty and those that violate it. They can be armed with either conventional warheads or nuclear ones.

Elbridge Colby, director of the defense program at the Center for a New American Security, said it was a challenge for Washington to balance Europe’s concerns about withdrawing from the treaty with the need to respond to the growing threat from China.

“It’s a hard sell for the Europeans because they see scrapping the treaty as pushing them into a further arms race with Russia without improving their security,” Mr. Colby said. “On the other hand, China is by far the most significant military threat to the U.S. and our allies, and we need to adjust to that.”