The pair held their first face-to-face talks since Biden took office on the sidelines of a G20 meeting expected to be dominated by the war in Ukraine.
The pair shook hands at the start of the meeting, with Biden saying the superpowers shared the responsibility to show the world that they can "manage our differences, prevent competition from becoming conflict".
The White House said he had told Xi that Washington would "continue to compete vigorously" with China, but "this competition should not veer into conflict".
Biden raised objections to China's "coercive and increasingly aggressive actions toward Taiwan," the White House said after three hours of talks aimed at avoiding conflict between the rival superpowers.
And he told Xi the world should encourage North Korea to act "responsibly", after a record-breaking series of missile launches by Pyongyang and growing fears of a new nuclear test.