RANCHO MIRAGE, Calif. — Even as they pledged to build “a new model” of relations, President Obama and President Xi Jinping of China ended two days of informal meetings here on 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.

Although the leaders of the world’s two biggest powers made no public statements on their second day of talks, 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 in detail.

From the outset, the White House said the purpose of the meetings here was not to announce new deals or understandings — “deliverables,” in diplomatic parlance — but to create a more comfortable relationship between Mr. Obama and Mr. Xi, who took full power in March, that could avoid plunging the two nations into escalating conflict.

Even so, 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 hydrofluorocarbons, known as HFCs, that are used in refrigerants and insulating foams.