Biden said he had met Chinese Premier Li Qiang at the G20 summit in New Delhi -- a meeting the White House had not announced -- and discussed "stability".
The president revealed the encounter in Hanoi, where earlier in the day he agreed a deal to deepen ties with Vietnam as Washington looks to bolster its network of allies around Asia and the Pacific in the face of Beijing's rising influence.
Washington and Beijing are at loggerheads on a range of global issues, and Biden accused China of seeking to bend the international order to its will.
"One of the things that is going on now is China is beginning to change some of the rules of the game, in terms of trade and other issues," Biden told a news conference.
Washington has invested heavily in building alliances as part of its Indo-Pacific strategy, including the Quad security dialogue with India, Australia and Japan, and the AUKUS pact with Britain and Australia.
But he insisted the United States is not seeking to box China in, but rather to establish clear ground rules for relations.
"I don't want to contain China. I just want to make sure we have a relationship with China that is on the up and up, squared away, everybody knows what it's all about," he said.
Chinese President Xi Jinping skipped the G20 as Beijing and Delhi tussle over territorial and other issues.
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