While there were few clear policy breakthroughs on cybersecurity, U.S. officials said Obama and Xi were in broad agreement over the need for North Korea to be denuclearized. And both countries expressed optimism that the closer personal ties forged between the two leaders during the California summit could stem the mistrust between the world powers.

Still, Obama’s national security adviser Tom Donilon said resolving cybersecurity issues would be “key to the future” of the relationship.

Obama told Xi that “if it’s not addressed, if it continues to be this direct theft of United States property, that this was going to be very difficult problem in the economic relationship and was going to be an inhibitor to the relationship really reaching its full potential,” Donilon said during a briefing with reporters following the summit.

In their own recap of the meetings, Chinese officials said Xi opposed all forms of cyberspying, but claimed no responsibility for attacks against the U.S.

“Cybersecurity should not become the root cause of mutual suspicion and frictions between our two countries. Rather, it should be a new bright spot in our cooperation,” said Yang Jiechi, Xi’s senior foreign policy adviser.

Yang said the two leaders “blazed a new trail” away from the two nations’ past differences and “talked about cooperation and did not shy away from differences.”

Obama and Xi met for about eight hours over the course of two days at the sweeping Sunnylands estate, marking a significant and unusual investment of time for both presidents. Their talks included a working dinner of lobster tamales, Porterhouse steak and cherry pie prepared by celebrity chef Bobby Flay, and a morning walk through the manicured gardens of the 200-acre estate on the edge of the Mojave Desert.

During their walk, the leaders stopped to sit on a custom-designed park bench made of California redwood that Obama presented to Xi as a gift.

The U.S. president told reporters that the talks were “terrific” as he and Xi walked side by side, both having ditched jackets and ties in a nod to the summit’s informal atmosphere. The leaders closed the summit in low-key style, with no formal statements to the press, just a private tea with Xi’s wife.

Obama and Xi did take a significant step toward tackling climate change, announcing that their countries had agreed for the first time to partner on reducing hydrofluorocarbons, a potent greenhouse gas used in refrigerators, air conditioners, and industrial applications.

The discussions on North Korea also proved promising, Donilon said, with the leaders agreeing that North Korea has to be denuclearized and that neither country will accept the North as a nuclear-armed state. North Korea is estimated to have a handful of crude nuclear devices, with some analysts putting its arsenal at four to eight plutonium bombs.

While China is Pyongyang’s strongest ally and economic benefactor, Xi has signaled a growing impatience with North Korea’s unpredictable and provocative nuclear threats.

“China has taken a number of steps in recent months to send a clear message to North Korea, including though enhanced enforcement of sanctions and through public statements by the senior leadership in China,” Donilon said.

U.S. officials are hoping that Xi, who took office in March, proves to be a new brand of Chinese leader. He has deeper ties to the U.S. than his predecessors, given that he lived in Iowa briefly as a visiting official and sent his daughter to college in the U.S.

The two leaders appear to have more in common than Obama had with former Chinese leader Hu Jintao, who often appeared stiff and formal in meetings. Both men are in their 50s and share a love of sports: swimming and soccer on Xi’s side, basketball and golf on Obama’s. Both are also married to glamorous, high-profile wives who have played a strong role in shaping their images.

While Xi’s wife accompanied him to California, Michelle Obama stayed in Washington. The White House said late Saturday that she wrote Xi’s wife a letter welcoming her to the United States and expressing regret for not seeing her this weekend.

Xi also appeared to relish in the more informal talks. An Obama administration official said he discussed at length growing up in the Chinese countryside during his country’s cultural revolution and how the experience impacted his perspective on China’s development. Xi also broke out a bottle of “Maotai,” a famous Chinese liquor, to toast Obama during Friday’s working dinner, according to the official, who insisted on anonymity in order to discuss the private meetings.

The two leaders will likely meet again in September, on the sidelines of an international economic summit in Russia. Xi also invited Obama to travel to China soon for a similarly informal round of one-on-one talks.

For Obama, the China summit marked the start of a heavy foreign policy-focused stretch that includes trips later this month to Europe and Africa. But domestic controversies are competing for his attention, including revelations that the National Security Agency has been secretly collecting massive amounts of data from U.S. phone and Internet companies.

The president sought to distinguish between the NSA actions and China’s alleged cyber intrusions, saying the two issues were separate and distinct. During a news conference with Xi on Friday night, Obama said he welcomed a debate on those differences.

During the question-and-answer session with reporters, Obama and Xi carefully avoided directly accusing each other’s nations of high-tech intrusions, though they acknowledged an urgent need to find a common approach on addressing the matter.

Obama said rapid cyber advances meant the two countries were in “uncharted waters.”

“We don’t have the kind of protocols that have governed military issues and arms issues, where nations have a lot of experience in trying to negotiate what’s acceptable and what’s not,” Obama said.

Xi, who called rapid technological advancements a “double-edged sword,” claimed no responsibility for China’s alleged cyberespionage. He said China was also a victim of cyberspying but did not assign any blame.

While Xi departed California Saturday afternoon, Obama planned to stay in California through the weekend, though he had no public events planned.

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By Julie Pace, AP White House correspondent