Washington (CNN) A Chinese spy ship is currently spying on a major US-led military exercise off the coast of Hawaii, the same exercise it was disinvited from due to US opposition to Beijing's militarization of features in the South China Sea.

"The US Pacific Fleet has been monitoring a Chinese navy surveillance ship operating in the vicinity of Hawaii outside US territorial seas," US Navy Capt. Charles Brown, a spokesman for US Pacific Fleet, said in a statement. "We expect this ship will remain outside of US territorial seas and not operate in a manner that disrupts the ongoing Rim of the Pacific maritime exercise."

China was disinvited from the exercise, known as RIMPAC, in May over what the Pentagon called China's "continued militarization of disputed features in the South China Sea," including the deployment of anti-ship missiles, surface-to-air missile systems and electronic jammers.

The spy ship arrived in the waters off Hawaii on July 11, and it has not entered the territorial seas of the United States, a US military official told CNN.

The Chinese ship's presence was also criticized by the exercise's combined forces maritime component commander, Chilean Commodore Pablo Nieman.

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