"We have to ensure that competition does not veer into conflict," Biden told Xi across a long wooden table as their delegations sat down for talks at the scenic Filoli country estate near San Francisco.
Xi responded by saying that "Planet Earth is big enough for the two countries to succeed."
The leaders of the world's largest economies have not met in person since they held in talks Bali in November 2022, and relations nosedived after the United States shot down an alleged Chinese spy balloon in February this year.
Since then, Beijing and Washington have been engaged in intense diplomacy to get the two leaders face to face and try to smooth over tensions on issues including Taiwan, sanctions and trade.
The hotly anticipated summit was expected to produce deals on resuming military to military contacts and cooperating to reduce the flow of the drug fentanyl to the United States.
But both leaders were clear the real focus is on cooling the tensions that have emerged against a backdrop of a long struggle for global primacy between the United States and an increasingly assertive China.
- 'Unbearable consequences' -
Their meeting at the Filoli estate, where the 1980s TV soap opera "Dynasty" was filmed, began with Biden sharing a smile and a handshake with Xi on a red carpet after the Chinese president stepped from a black limousine.
The pair shook hands again for the cameras on the steps of the brick mansion, this time with more somber expressions on their faces.
The two leaders then headed inside for painstakingly choreographed, closed-door talks in a frescoed ballroom.
"We've known each other for a long time. We haven't always agreed, which is not a surprise to anyone, but our meetings have always been candid and straightforward and useful," Biden said told Xi.
"I think it's paramount that you and I understand each other clearly, leader to leader, but (with) no misconceptions or miscommunication."
Biden added that they would discuss global challenges including climate change and artificial intelligence.
Xi responded that "conflict and confrontation has unbearable consequences for both sides."
"For two large countries like China and United States, turning their back on each other is not an option," he said.
But in a jab at US calls over human rights and other issues, Xi said it was "unrealistic for one side to remodel the other."
Biden was to give a solo press conference at 4:15 pm (0015 GMT Thursday) to discuss the Xi meeting, which was being held on the sidelines of the APEC summit in San Francisco.
- Taiwan tensions -
Neither leader in their opening remarks mentioned the elephant in the room -- the issue of Taiwan, a self-ruling democracy over which Beijing claims sovereignty and which it has not ruled out seizing by force.
Biden was expected to tell Xi that the United States will stick to its "One China" policy that emphasizes it does not support Taiwanese independence, but that it will continue to give Taiwan military aid, White House National Security Council spokesman John Kirby said.
Despite lukewarm expectations, the two countries have trailed a series of possible wins from Xi's first visit to US soil since he was hosted by then-president Donald Trump in 2017.
There were hopes of "progress" on cooperation to limit Chinese exports of ingredients for fentanyl, the opioid drug sweeping America. The two leaders were additionally expected to discuss the Israel-Hamas conflict and the Ukraine war.
Russia, a partner of China in what Washington sees as a growing authoritarian alliance, welcomed the meeting, with the Kremlin calling the talks "important for everyone."
For his part Xi was expected to push for an end to trade curbs, with the Chinese economy struggling to shore up growth after its tough zero-Covid policy.
The Chinese leader was to host a dinner with US executives after the summit.
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