The summit was billed as a chance for the two men to get to know each otherEconomic and environmental issues dominated the second day of a summit between US President Barack Obama and Chinese leader Xi Jinping, but cyber-security was also on the agenda.
The US wants China to move towards a more consumer-led economy, narrowing the trade gap.
Mr Obama said on Friday the US wanted nations to play by the same rules while Mr Xi spoke of a new blueprint.
But Mr Obama added that cyber-security was an area of growing importance.
The US president has in the past criticised what he called Chinese state-sponsored cyber attacks on the US.
However, last week he defended US phone and web surveillance programmes.
The two leaders spent nearly six hours together on Friday and another three hours on Saturday morning.
Sunnylands
- Built in the 1960s in Rancho Mirage, California, as a home for Walter and Leonore Annenberg
- 25,000-sq ft house was designed by renowned American architect Quincy Jones
- 200-acre estate includes 11 lakes, a tennis court, and a nine-hole golf course
- In 2001, the Annenbergs directed that the estate be available to serve as a sanctuary for high-level national and world leaders seeking privacy and peace for resolving international issues
- Has hosted seven US presidents, British royalty and other world leaders
- While briefly appearing for a stroll together on Saturday, Mr Obama described their progress as "terrific".
Mr Xi later left the sprawling Sunnylands estate and the White House issued a statement saying the two nations had agreed to work together for the first time to reduce hydrofluorocarbons - a potent greenhouse gas.
A spokesman for the Chinese President said the summit had been very wide-ranging and candid and had included the issues of cyber security and climate change.
He said China emphasised the importance of maintaining world peace and said the two countries wanted to forge a new model relationship.
Speaking after his first session of talks with Mr Xi on Friday, Mr Obama described cyber-security as "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," he said.
On Friday, the Guardian newspaper published what it described as a US presidential order to national security and intelligence officials to draw up a list of potential overseas targets for US cyber-attacks.
The White House has not commented on the report.
The summit was the first meeting between the two men since Mr Xi became president in March.
It was billed as a chance for the two to get to know each other.
The BBC's North America editor, Mark Mardell, says the series of leaks about US national security may embarrass President Obama enough to make the summit a little less pious, and a bit more realistic.
Relaxed start
On Friday, the two men - looking relaxed and informal - met and shook hands under a shaded walkway at the estate just outside Palm Springs.
Mr Xi said he and Mr Obama were meeting "to chart the future of China-US relations and draw a blueprint for this relationship".
For his part, Mr Obama said the US welcomed the rise of a peaceful China and wanted "economic order where nations are playing by the same rules".
The US and China are the world's two largest economies. The US runs a huge trade deficit with China, which hit an all-time high of $315bn (£204bn) last year.
Last week, the Chinese firm Shuanghui agreed to buy US pork producer Smithfield for $4.7bn (£3.1bn) - the largest takeover of a US company by a Chinese rival.
The deal highlights the growing power of Chinese firms and their desire to secure global resources.
US producers want China to raise the value of its currency, the renminbi, which would make Chinese goods more expensive for foreign buyers and possibly hold back exports.
Beijing has responded with a gradual easing of restrictions on trading in the renminbi.
Intellectual property is also an area of concern for US firms.
A report last month by the independent Commission on the Theft of American Intellectual Property put losses to the US from IP theft at as much as $300bn (£192bn) a year. It said 50-80% of the thefts were thought to be by China.
Ahead of the summit, White House officials told reporters hacking would be raised, amid growing concern in the US over alleged intrusions from China in recent months.
Last month the Washington Post, citing a confidential Pentagon report, reported that Chinese hackers had accessed designs for more than two dozen US weapons systems.
The US also directly accused Beijing of targeting US government computers as part of a cyber-espionage campaign in a report in early May.
bbc.com