Speaking at Arizona State University before a trip aimed at underscoring President Barack Obama's strategic "rebalance" towards Asia, Carter said the US remained committed to helping maintain peace in the region.
But the Pentagon chief said Washington was troubled by China's activities in the realms of defence spending, cyber-space and regional territorial spats.
"We and many other countries are deeply concerned about some the activities China is undertaking," Carter said.
An escalation of tension between the United States and China need not be inevitable, however, Carter said.
Also Read
"The US and China are not allies but we don't have to be adversaries. A strong constructive US relationship is essential for global security and prosperity," he said, acknowledging that Sino-US relations would be "complex" as both nations sought to "compete and cooperate."
Carter noted agreements signed between China and the US last year aimed at building confidence between the two superpowers and said another pact to prevent "dangerous air-to-air encounters" would be completed later this year.
The Obama administration's "rebalance," he argued, was "helping create the right incentives and conditions to encourage China to play by the rules of principled international order."
Carter's trip to Asia is the first of two scheduled in the coming months. He will stop in Tokyo and Seoul before meeting the head of US Pacific Command in Hawaii on his way back to the US.
Carter will return to the region in May for the annual Shangri-La security conference in Singapore followed by a visit to India, which he has worked closely with in the past to bolster defense ties.