U.S. President Barack Obama and his Chinese counterpart Xi Jinping launched straight into discussing thorny issues at an informal summit and may delve deeper when they meet again on Saturday.
The two-day meeting at a desert retreat near Palm Springs, California, was meant to be an opportunity for Obama and Xi to get to know each other, Chinese and U.S. officials have said, and to inject some warmth into often chilly relations while setting the stage for better cooperation.
The first day yielded no major breakthroughs or concrete announcements.
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After more than two hours of discussions, Xi and Obama said they had agreed on the need to work together to tackle cyber-security issues, a major irritant in bilateral ties as U.S. accusations of Chinese hacking intensify.
They also agreed on the importance of improved military-to-military ties, an area hindered in the past by mistrust and poor communication.
"We are more likely to achieve our objectives of prosperity and security of our peoples if we are working cooperatively rather than engaged in conflict," Obama told reporters.
Ties between Beijing and Washington have been buffeted in recent months by strains over trade disputes, North Korea, human rights and each country's military intentions.
Obama said the two countries must strike a balance between competition and cooperation to overcome the challenges that divide them, and Xi pushed for a relationship that takes into account China's ascendancy.
Xi is expected to voice discomfort over Washington's strategic pivot toward Asia, a military rebalancing of U.S. forces toward the Pacific that Beijing sees as an effort to hamper its economic and political expansion.
Obama and Xi are due to hold a total of more than five hours of talks in Sunnylands, a 200-acre (81-hectare) estate on Bob Hope Drive that has hosted presidents including Ronald Reagan and Bill Clinton and where afternoon June temperatures soar to 110 degrees Fahrenheit (43 Celsius) or more.
Obama will be looking to build on growing Chinese impatience with North Korea over its nuclear and missile programs, a shift that could bring Beijing - the closest thing Pyongyang has to an ally - closer to Washington's position.
"I think it's perhaps the most important meeting that they'll have in their tenure," said Paul Haenle, former China director on the NSC and director of the Carnegie-Tsinghua Center for Global Policy in Beijing.
"The biggest problem with the relationship is that we haven't had the deep and personal engagement at the very senior level that's required now to move forward to take the relationship to a new point."