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Harris, who has been at the helm of the most expansive US military command for three years, hammered home points he's made repeatedly during his term.
"North Korea remains our most imminent threat and a nuclear-capable North Korea with missiles that can reach the United States is unacceptable," he said.
However he added, "China remains our biggest long-term challenge. Without focused involvement and engagement by the United States and our allies and partners China will realize its dream of hegemony in Asia."
Responding to Harris's comments Thursday, Chinese Foreign Ministry spokeswoman Hua Chunying said the admiral was "obsessed with hegemony" because he fears others are trying to steal it from the US.
"The US military presence in the South China Sea far exceeds the total of China and other coastal countries," Hua said, calling US accusations of militarization "like a thief crying, 'Stop, thief!'"
China's deployments and building programs in the South China Sea are part of its self-defense, Hua added.
Harris spoke alongside US Secretary of Defense James Mattis, who stopped off in Hawaii on his way to Singapore for a high-profile security forum, where issues relating to the South China Sea and North Korea will be discussed.
It is unclear what role Harris will play in talks with Pyongyang leading up to a hoped-for summit between US President Donald Trump and North Korea leader Kim Jong Un in Singapore on June 12. Harris' nomination went to the Senate on May 18 ahead of his expected confirmation.
While Harris has always been a hawk on North Korea during his term at Pacific Command, he has also issued warnings on China as Beijing has pursued a more muscular military posture in the Pacific and established a military presence on man-made islands in areas the US and its allies contend are international waters.
Standing alongside Secretary of State Mike Pompeo at a news conference in Washington on May 23, Chinese Foreign Minister Wang Yi called the US decision "unhelpful."
"We find that a very unconstructive move ... It's unhelpful to mutual understanding between China and the US. We hope the US will change such a negative mindset," he said.
In Hawaii Wednesday, Mattis said, "we should cooperate with Beijing where we can but stand ready to confront them where we must."
Harris also warned his successors to keep an eye on Moscow, saying Russia is trying to act as "the spoiler" in the Indo-Pacific.
"A geopolitical competition between free and repressive visions of world order is taking place in the Indo-Pacific," Harris said.
"Great power competition is back and I believe we're approaching an inflection point in history.... Freedom and justice hang in the balance."
CNN's Tim Schwarz contributed to this report.