WASHINGTON—China seized a U.S. Navy underwater drone in the South China Sea and the Pentagon demanded it back, raising a new point of tension between U.S. and Chinese military forces in the disputed waters as relations between the countries enter uncharted territory.

“It’s ours, it was clearly marked, we want it back, and we don’t want this to happen again,” said Capt. Jeff Davis, a Pentagon spokesman.

The incident on Thursday occurred days after President-elect Donald J. Trump raised China’s ire by suggesting his administration could abandon a bedrock agreement on Taiwan’s status that has kept peace in the area for decades. Mr. Trump’s suggestion that the U.S. would maintain its position on Taiwan only if China makes concessions to American interests came after he broke decades of diplomatic protocol by accepting a phone call from Taiwan’s president, hitting one of Beijing’s most sensitive issues.

It also came as a Washington-based think tank reported China had installed antiaircraft weapons and other small arms on all seven of its reclaimed islands in the South China Sea, where China has built artificial islands and laid claim to a vast swath of maritime territory, to the dismay of neighbors and U.S. officials. China’s actions have raised concerns in the U.S. that Beijing is planning to enforce broad and disputed claims over the sea, a hub that sees more than $5 trillion in trade transit its waters annually. China’s Defense Ministry said on its website Thursday that any reef construction was mainly for civil use, and that any military facilities “are mainly for defense and self-defense, which is appropriate and legal.”

In the latest incident, the U.S. Naval Ship Bowditch, which has a civilian commander, was retrieving two underwater drones about 50 nautical miles northwest of Subic Bay in the Philippines. It was being shadowed by a Chinese ship, a Dalang 3, a typical occurrence when U.S. ships navigate those waters, Navy and defense officials say.