Mr Biden appeared to be referring to Washington's longstanding "one China" policy under which it recognises China rather than Taiwan.
However, this agreement also allows Washington to maintains a "robust unofficial" relationship with Taiwan.
The announcement comes amid escalating tensions between Taiwan and Beijing.
It has sent "record numbers" of military jets into Taiwan's air defence zone for four consecutive days, which some analysts say could be seen as a warning to Taiwan's president ahead of the island's national day.
Taiwan has its own constitution, military, and democratically elected leaders, and considers itself a sovereign state.
Beijing however, views Taiwan as a breakaway province and has not ruled out the possible use of force to achieve unification with the island.
The "One China" policy, which Mr Biden and Mr Xi are believed to have referred to, is a key cornerstone of Sino-US relations but is distinct from the One China principle, whereby China insists Taiwan is an inalienable part of one China to be reunified one day.
"I've spoken with [Mr] Xi about Taiwan. We agree ... we'll abide by the Taiwan agreement," said President Biden. "We made it clear that I don't think he should be doing anything other than abiding by the agreement.