SINGAPORE — Acting Defense Secretary Patrick Shanahan sought to lower the temperature on the Trump administration’s stew of hostilities with China on Friday, saying it was imperative to look for ways for the two competing militaries to “create upside” in their relationship, even in the middle of a trade war.

Mr. Shanahan barely mentioned China by name during a speech to a gathering of Asian military officials on Saturday, although he warned Beijing that “behavior that erodes other nations’ sovereignty and sows distrust of China’s intentions” should stop, in a clear reference to China’s militarization of disputed islands in the South China Sea.

“The United States does not seek conflict, but we know that having the capability to win wars is the best way to deter them,” Mr. Shanahan said. At the same time of Mr. Shanahan’s speech, the Pentagon released a report criticizing what it characterized as China’s aggressive moves in the region.

In fact, the deep tensions between Washington and Beijing showed no signs of abating on Friday. China remained on track to impose retaliatory tariffs of 20 to 25 percent on a slew of American products starting Saturday. That move makes China a full combatant in the trade war launched by President Trump.