RANCHO MIRAGE, Calif. — Even as they pledged to build “a new model” of relations, President Barack Obama and President Xi Jinping of China ended two days of informal meetings here Saturday moving closer on pressuring a nuclear North Korea and addressing climate change, but remaining sharply divided over cyberespionage and other issues that have divided the countries for years.

Broadly, both leaders urged cooperation, not conflict. Although they made no statements Saturday, their disagreements — over cyberattacks as well as arms sales to Taiwan, maritime territorial disputes in the South China Sea and manipulation of the Chinese currency — spilled into the open when senior officials from both countries emerged to describe the meetings.

The White House announced that the two countries had reached at least one concrete accord that environmentalists welcomed as a potential step in combating climate change. China and the United States agreed to discuss ways to reduce emissions of hydroflourocarbons, known as HFCs, that are used in refrigerants and insulating foams.

Obama and Xi also found areas of agreement over North Korea. Obama’s administration has welcomed China’s new assertiveness with its neighbor and ally, believing that it reflects a new calculation that a constant state of crisis on the Korean Peninsula is destabilizing for the Chinese as well. “They agreed that North Korea has to denuclearize,” national security adviser Tom Donilon said.

On the most contentious issue in recent months — American accusations that Chinese corporations linked to the military had pilfered military and economic secrets and property in cyberspace — the officials seemed to speak past each other. That dominated Saturday’s talks here at a secluded estate, but ended without a clear acknowledgment by Xi of any culpability.

China’s state councilor, Yang Jiechi, said China strongly opposed hacking and was itself a victim, while Donilon warned that the threat from China threatened to constrain the spirit of partnership Obama and Xi publicly declared they wanted. Obama warned that if the hacking continued, Donilon said, it “was going to be a very difficult problem in the economic relationship.”

Secretary of State John Kerry, who attended the meetings, has previously announced that the two countries would discuss cyberspying as part of the annual meetings known as the Strategic and Economic Dialogue, to be held in Washington in July.