The US navy’s challenge last week to China’s sovereignty claims in the South China Sea was not designed as a military threat, the head of US Pacific military forces has said in a mostly upbeat speech about prospects for preventing US-China disputes from escalating to conflict.

In separate high-level meetings of military officials from the two countries later on Tuesday – one in Beijing and one in Malaysia – top Chinese officials again expressed their country’s pique over the US warship sailing past Chinese-built islands, while also expressing hope that the two sides could build further trust.

Speaking at a university in the Chinese capital, Adm Harry B Harris Jr cited a recent statement by the US defense secretary, Ash Carter, that the international order “faces challenges from Russia and, in a different way, from China, with its ambiguous maritime claims”, including Beijing’s claim to nearly all of the South China Sea.

However, Harris said the decision to send the USS Lassen, a guided-missile destroyer, into the South China Sea last week near Subi Reef, within the 12-nautical-mile (22km) territorial limit claimed by China, was meant to demonstrate the principle of freedom of navigation.

“I truly believe that these routine operations should never be construed as a threat to any nation,” Harris said, according to his prepared remarks. “These operations serve to protect the rights, freedoms and lawful uses of the sea and airspace guaranteed to all nations under international law.”

China at the time protested against the Lassen patrol, calling it a “deliberate provocation”, and sent two warships to shadow the US vessel and issue warnings. Although China labeled the action illegal, international law allows warships to transit other countries’ territorial seas under the principle of “innocent passage”.

In a meeting later on Tuesday in the Malaysian capital of Kuala Lumpur, the Chinese defense minister, Chang Wanquan, reiterated China’s view that the Lassen patrol was illegal, according to two senior US defense officials who attended the meeting and briefed reporters afterward on condition of anonymity.

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The US officials said Chang told Carter that China’s activities in the South China Sea are mainly defensive in nature, and that for China there is a “bottom line” on US challenges to China’s territorial claims there. The officials said Chang did not elaborate, and his remark was not interpreted as a threat of any kind.

Carter and Chang spoke for 40 minutes on the sidelines of an Asia defense ministers gathering. Carter welcomed President Xi Jinping’s statement at the White House in September that China “does not intend to pursue militarization” of reclaimed islands in the South China Sea, but Chang did not elaborate on Chinese intentions, the defense officials said.

Carter’s press secretary, Peter Cook, said the defense secretary accepted a Chinese invitation to visit Beijing next spring.

At the meeting on Tuesday in Beijing between Harris and Gen Fang Fenghui, chief of general staff for China’s military, Fang said the sailing of the US vessel had cast a shadow on the talks, and reiterated Chinese claims to South China Sea territory since “ancient times”.

“Just before your visit, regardless of the solemn representations of the Chinese side, the US sent a naval vessel to cruise near the islands of China’s Nansha Islands, which has created a disharmonious atmosphere for our meeting, and this is very regretful,” he said in remarks in front of reporters at the defense ministry in Beijing.

Fang went on to say: “It is my hope that we can enhance mutual understanding and trust and remove negative effects.”

Facebook Twitter Pinterest The alleged land reclamation of China at Subi reef, which the US does not recognize as a legitimate island for the purposes of establishing territorial waters. Photograph: Pool/Reuters

In his speech earlier on Tuesday, Harris said the US does not want disagreements to interfere with opportunities for building closer military-to-military ties with China. He cited recent advances, such as a Military Maritime Consultative Agreement on measures to improve safe military operations in the Asia-Pacific.

Harris has been outspoken in his criticisms of China’s land reclamation in the South China Sea. In March, he said China was “creating a great wall of sand” that was causing serious concern about militarizing reefs and artificial islands in an area of competing territorial claims by several countries. China and five other governments claim the South China Sea either in part or in whole.

The US does not recognize the man-made features, including Subi Reef, as legitimate islands entitled to territorial seas, and US officials say they plan to patrol near them on a regular basis to enforce that view. China has reclaimed approximately 2,000 acres (809 hectares) of land in the Spratly island chain since last year, and is now adding harbors, housing and airstrips.

Harris spoke on Tuesday to Stanford University students studying at Peking University in Beijing. He is in Beijing on his first visit as commander of US Pacific Command, which is responsible for US military operations throughout the Asia-Pacific.

In his remarks, the admiral was mostly upbeat in his assessment of prospects for improving relations with China, saying he did not subscribe to the pessimistic view that a conflict was inevitable. While saying that as a military commander he is required to “look through a darker lens and drink through a glass half-empty”, he emphasized areas of mutual US-China interest and ways in which the two countries are cooperating.

“I agree with many of my Chinese counterparts who have emphasized cooperation over confrontation,” Harris said, according to a copy of his prepared remarks provided to reporters traveling with the defense secretary in Malaysia.