By Liz Lee, Yukun Zhang and Xiuhao Chen

BEIJING, May 14 (Reuters) - China’s President Xi Jinping hailed on Thursday a “new positioning” of ties with the United States that envisages cooperation with measured competition, following his summit with President Donald Trump.

Xi said both leaders agreed that building a constructive, strategically stable relationship would guide ties in the next three years and beyond, according to a Chinese foreign ministry statement.

Xi described such ties as based primarily on cooperation but with measured competition for “a normal stability in which differences are controllable, and a lasting stability in which peace can be expected”, the ministry added.

He called for both countries to widen exchanges and cooperation in trade, health, agriculture, tourism, people-to-people exchanges, and law enforcement, it said.

Even as Xi talked up cooperation, he stressed “utmost caution” by the United States in handling the issue of Taiwan, the democratically governed island claimed by China, although Taipei rejects the contention.

“If handled poorly, the two countries could collide or even enter into conflict, pushing the entire China-U.S. relationship into an extremely dangerous situation,” the Chinese leader said.

(Reporting by Liz Lee and Beijing newsroom; Editing by Christian Schmollinger and Clarence Fernandez)