Yang, joined by Chinese Defence Minister Wei Fenghe, are holding a security and diplomatic dialogue with the United States in Washington on Friday.
Reflecting growing US concerns about the Chinese cyber threat, a senior USA intelligence official on Thursday accused China of violating a 2015 agreement aimed at stopping cyber espionage through the hacking of government and corporate data.
And a high-profile meeting could occur in the coming days, when U.S. Vice President Mike Pence travels to the Asia-Pacific Economic Cooperation (APEC) summit in Papua New Guinea.
Calling Kissinger an old friend of Chinese people, Xi hailed the "historic contribution" he has made to China-U.S. relations.
Speaking at a news conference after bilateral talks with the United States officials, Yang Jiechi, China's highest-ranking diplomat and director of the Office of Foreign Affairs of the Central Commission of the Communist Party, said that Washington should refrain from actions that undermine stability in the South China Sea.
Pompeo said the U.S. had also expressed concern about China's approach to Taiwan, particularly its efforts to limit worldwide engagement with the breakaway province. "Rather we want to ensure that China acts responsibly and fairly in support of security and prosperity of each of our two countries". China and the US should better understand each other and enhance communication to expand mutual benefits while managing disagreements.
The talks were due to be held in Beijing last month but were postponed after Washington announced new arms sales to Taiwan, and after a Chinese destroyer came close to the USS Decatur in late September in what the U.S. Navy called an "unsafe and unprofessional maneuver". "The US should stop sending its vessels and aircraft close to" Chinese territory in the South China Sea, the Chinese minister said.
A senior administration official said Pence's meetings with regional leaders were still being planned, but a meeting between Pence and Chang, Taiwan's envoy to APEC, was not being ruled out.
The mention of the so-called maritime militia, which the Pentagon says is "the world's largest" and "has organizational ties to, and is sometimes directed by, China's armed forces", was unusual in that it is rarely mentioned in formal, high-level talks.
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US officials said they would not halt so-called freedom-of-navigation patrols that are aimed at ensuring countries do not restrict traffic in worldwide waters. That is the right of preservations and self-defence that worldwide law has provided for sovereign state that has nothing to do with militarization.
The US has since pushed back, insisting it will continue to "fly, sail and operate wherever worldwide law allows".
"The Chinese side has kept the channel of dialogue open".
"This will only get more acute over time", he said. Trump has slapped tariffs on $250 billion in Chinese products, in a push to narrow the USA trade deficit and push back against what the US views as predatory Chinese tactics on the high technology industry.
While the Washington talks focused on security, trade is at the heart of tensions between the world's two biggest economies.
China and the U.S. have put tariffs on hundreds of billions of dollars of each other's goods and Trump has threatened to set tariffs on the remainder of China's US$500 billion-plus exports to the United States if the dispute can not be resolved.
Yang voiced hope for a quick resolution. "A trade war, instead of leading to any solution, will only end up hurting both sides and the global economy", he added.
"The door to negotiation remains open".